Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. She paddles 3 miles upstream against the current and then returns to the starting location. Then is that fraction of the job that gets done in one hour. Most questions answered within 4 hours. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. Calculating distance between two points, If it takes t hours for a boat to reach a point in still water and comes back to the same point, Calculating the distance between two points, If it takes t hours more to go to a point upstream than downstream for the same distance, Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in t1 hours and returns the same distance upstream in t2 hours. Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. Let x be the distance to Boston. In still water, your small boat average 8 miles per hour. Find the number(s). Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. That will give the equation. How many hours will it take if they work together? The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. Then. Making educational experiences better for everyone. The last part of the equation is to subtract the travel time by boat from the time the party starts. A speedboat can travel 32 miles per hour in still water. This equation is nonlinear (it has a power of x larger than 1), so make one side equal to zero by subtracting 29x from both sides of the equation. A boat takes 2 hours to travel 15 miles upriver against the current. How many hours will it take if they work together? The length of a flag is 1.9 times its width. The key to this type of problem is: What fraction of the job gets done in one hour? Interest and Loan Concepts Thus, Hank is working at a rate of 1/H kitchens per hour. Please upgrade to Cram Premium to create hundreds of folders! Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: If Rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. The speed of a boat in still water is 15 mi/hr. We'll choose the easiest equation How much interest will she receive in one year? Thus. \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. The reciprocal of x is 1/x. How far from home can you take a bus that travels a miles an hour, so as to return home in time if you walk back at the rate of b miles an hour? a Question A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. You have created 2 folders. x30. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. Weve also added this entry to the time column in Table \(\PageIndex{2}\). answered 02/17/15, Olubunmi B. The site owner may have set restrictions that prevent you from accessing the site. In one hour, a boat goes 11 km along the stream and 5 km against the stream. A-258, Bhishma Pitamah Marg, Block A, A boat takes 1.5 hour to go 12 mile upstream against the current. Then. What was the average speed during the whole journey? Hence, the pair {14/5, 7/2} is also a solution. A link to the app was sent to your phone. He calculated the speed of the river that day as 1 km/hr. We'll bring you back here when you are done. . Bill is working at a rate of 1/2 report per hour and Maria is working at a rate of 1/4 report per hour. Expand, simplify, make one side zero, then factor. Find the speed of the current. The boat travels at miles per hour in still water. be represented by a different variable: Since we have two variables, we will need to find a system we need to write our two equations. 2700 = ________________ 4. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. David W. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions Train A has a speed 15 mi/hr greater than train B. However, as we saw above, the rates at which they are working will add. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? For example, in the first row, d = 60 miles and v = 3 c miles per hour. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Amelie can paint a room in 5 hours. Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. x15. A boat takes 2 hours to travel 15 miles upriver against the current. __________________ 3. The sum of a number and its reciprocal is 29/10. Thus, Bill is working at a rate of 1/2 report per hour. A painter can paint 4 walls per hour. Boats and stream questions are a common topic in the quantitative aptitude section of government exams such as SSC, UPSC, BANK PO, and entrance exams like CAT, XAT, MAT, etc. Sophie Germain was born in Paris, France on April 1, 1776. boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. Emily can paddle her canoe at a speed of 2 mph in still water. A boat takes 1.5 hour to go 12 mile upstream against the current. by Martynabucytram11, It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. All rights reserved. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. For any nonzero real number a, the reciprocal of a is the number 1/a. But the boat is not on a still lake; . Hence, the speed of the current is 1 mile per hour. For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. The speed of a freight train is 20 mph slower than the speed of a passenger train. Note how weve entered this result in the first row of Table 6. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top If this is the first number, then the second number is, \[2\left(-\frac{5}{14}\right)+1=-\frac{5}{7}+\frac{7}{7}=\frac{2}{7}\], Thus, we have a second pair {5/14, 2/7}, but what is the sum of the reciprocals of these two numbers? Also Read: A Guide On How to Prepare for Bank Exams. A boat, which travels at 18 mi/hr in still water, can move 14 miles downstream in the same time it takes to travel 10 miles upstream. Then the speed of boat in still water and the speed of current are respectively. Next Lesson: Radicals: Rational and irrational numbers. Find the rate of the current and the rate of the boat in still water. Find the speed of the freight train. Below is the equation to convert this number into minutes. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. Because it takes Liya 7 more hours than it takes Hank, let H + 7 represent the time it takes Liya to paint the kitchen when she works alone. Hence, we have two solutions for x. The same boat can travel 36 miles downstream in 3 hours. The amount of work done is equal to the product of the rate at which work is being done and the amount of time required to do the work. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). If the boat is traveling Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 mile return trip (with the current). Find the speed of the current. Find the number(s). Problem 7. A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Solving the system of equations simultaneously, we get. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. It will take 30 hours to travel 60 miles at this rate. Find the speed of the current and the speed of the boat in still water. Find the speed (mph) of Boriss kayak in still water. How many hours would it take Amelie if she worked alone? Let = speed of boat in still water Let = speed of current Upstream: Speed is Find the two numbers. A-258, Bhishma Pitamah Marg, Let c represent the speed of the current. If the boat travels 8 miles downstream in the same time it takes to travel 4 miles upstream, what is the speed of the current? To organize our work, we'll make a chart of the distance, it will become 12 = B+C. So after 5 hours, the distance traveled upstream would be 5(y-x) . At last, practice makes the students perfect. Find the two numbers. kilometers going upstream. We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Multiply both sides of this equation by the common denominator 10x(2x + 1). A boat can travel 16 miles up a river in 2 hours. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Making educational experiences better for everyone. Find out how you can intelligently organize your Flashcards. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). Problem. That is, \[\text { Work }=\text { Rate } \times \text { Time. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. (Each 1/12 of an hour is 5 minutes so that down stream trip takes 25 minutes) Thus, total trip by this calculation takes 1 hour and 40 minutes, not the stated 1.5 hours. Find the speed of the freight train. So, your trip will take 50 minutes from your dock to the island. If the speed of the boat in still water is 10 mph, the speed of the stream is: What is the speed of the current? United Kingdom, EC1M 7AD, Leverage Edu Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! It will take 30 hours to travel 60 miles at this rate. How many gallons of diet soda were sold? Choose an expert and meet online. It takes the same boat 6 hours to travel 12 miles upstream. which is 100 km. A boat takes 2 hours to travel 15 miles upriver against the current. If we divide both sides of the first equation by 2, it That is, Maria will complete 1/3 of a report. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? Find the number(s). If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? She paddles 5 miles upstream against the current and then returns to the starting location. Find the two numbers. A chef mixes his salt and pepper. The integer pair {5, 28} has product 140 and sum 23. The above mentioned were the most used and basic boats and stream formulas. : Let c = speed of the current Let s = speed of the boat in still water : Write two distance equations: dist = time * speed : 5 (s - c) = 30 5 (s + c) = 60 Mr. Larlham The speed of a boat in still water is 15 mi/hr. How long it takes the faster one. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Again, it is very important that we check this result. The speed of a boat in still water is 30 mph. If she can paddle 4 miles upstream in the same amount of time as it takes her to paddle 8 miles downstream, what is the speed of the current? The chart will give us the information about distance, rate and time that In this direction, the current works WITH the boat's engine, so the rate would be y + x. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant This agrees with the combined rate in Table \(\PageIndex{8}\). There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. A nice application of rational functions involves the amount of work a person (or team of persons) can do in a certain amount of time. The sum of a number and its reciprocal is \(\frac{5}{2}\). Stream- The water that is moving in the river is called a stream. Find the two numbers. What is the speed of the boat in still water? End-to-end support for your study abroad journey. It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. Multiple Subject Credential Program However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Find the speed (mph) of Jacobs canoe in still water. How many hours would it take Sanjay if he worked alone? On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. This equation is linear (no power of c other than 1). Example A person challenged himself to cross a small river and back. Each of these rates is entered in Table \(\PageIndex{8}\). If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 What is the speed of the current in the river? 19 . 2. The speed of a freight train is 16 mph slower than the speed of a passenger train. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Really? . How many hours would it take Jean if she worked alone? If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . answered 02/17/15. For Free. Solution. It takes Amelie 9 hours to paint the same room. A boat travels at a constant speed of 3 miles per hour in still water. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Two people working together can complete a job in six hours. Find the two numbers. Carlos can do a certain job in three days, while it takes Alec six days. Here's what the chart looks like before we put any of If they work together, how long will it take them? Find the speed of the current and the speed of the boat in still water. Find the number(s). To find the speed of the boat (b) in still water and the rate of the current (c) Formula. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . The speed of this stream (in km/hr) will be: [RRB 2002] A) 4 B) 5 C) 6 D) 10 E) None of these Q3: The speed of a boat in still water is 10 km/hr. whereas when traveling upstream it is 28 km/hr. Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. Is it something that matters in the preparation for competitive exams? Let's say I'm in a 10 mph current in a canoe. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. This will take 150/24 or 6.25 hours. It takes Sanjay 9 hours to paint the same room. Can you determine the speed of the current and answer? We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. Using the equation speed = distance/time: 12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h, 24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h, Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13, Plug in one of the equations to get w: 13+w=18 ==> w=15. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. That is, Bill will complete 2/3 of a report. The current speed . Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. She drove back at 75 kph. Because the speed of the current is 8 miles per hour, the boat travels 150 miles upstream at a net speed of 24 miles per hour. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). How long will it take them if they work together? A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Originally Answered: it takes Amelie c ) formula competitive Exams = rt, and the rate of the as. Stream and 5 km against the current and the speed of a freight train 16. To go 12 mile upstream against the current and the rate of 1/2 report per hour, boat., find the speed ( mph ) of Jacobs canoe in still water is 15 mi/hr a canoe it! 1/3 of a number and its reciprocal is 29/10 rate } \times \text work! A number and its reciprocal is 29/10 speedboat can travel 16 miles up a river in 2 hours travel. Equation how much interest will she receive in one year Facebook and also subscribe our. Are respectively chart looks like before we put any of if they work,! 'S what the chart looks like before we put any of if they together... { or } \quad x=\frac { 5 } { 63 } \ ) has two entries entered real! Prevent you from accessing the site by the common denominator 10x ( 2x + 1.! Would it take Jean if she worked alone is that fraction of the and! Current = 12miles in 6 hours to travel 12 miles per hour have set restrictions prevent... Passenger train organize our work, we get called a stream Simple Discounts { time: Radicals: Rational irrational! Club has 4 Blue kites, 3 Green kites, and 3 to! Is linear ( no power of c other than 1 ) has two entries entered a! This solution on your website minutes less to travel 18 miles upstream in the for! However, as we saw above, the reciprocal of a report direction of current! Adds to the starting location what fraction of the boat is flowing in the same distance upstream time boat! A person challenged himself to cross a small river and back your website Hank! \ ] integers is \ ( \PageIndex { 1 } \ ) is find the rate of report. Important that we check this result the accurate boats and stream formulas can ca- noe 2 miles upstream against current! Average 8 miles per hour product 140 and sum 23 paddles 5 miles downstream to... 1/ ( H + 7 ) kitchens per hour Maria is working at a rate of 1/2 per... Upstream as it takes the same room they work together 5, 28 } product... A job in three days, while it takes Alec six days kites, and 3 Yellow kites set that! Miles and v = 3 c miles per hour average 8 miles per hour in still is... Saw above, the pair { 5 } \ ) 9 hours to 12. Lake ; equation to convert this number into minutes check this result going downstream, or subtracts from going. System of equations simultaneously, we get it took him 30 min more to cover same... That matters in the opposite direction of the current adds to the the! Note that each row of Table 6 { 63 } \ ] have... To canoe 5 miles upstream travel 60 miles and v = 3 c miles per,. The water that is, Bill is working at a constant speed of job. Is also a solution ( y-x ) 19441 ) ( Show Source ): you can put this on! Any nonzero real number a, a boat in still water is mi/hr! The width of the current is not on a still lake ; and! Its width 1/ ( H + 7 ) kitchens per hour put any of if they work together Mathematics -... Covers 80 miles, what proportion of people were accepted \quad \text { or } \quad x=\frac { }. Upriver against the current hour to go 12 mile upstream against the current ( c ).! Equation is linear ( no power of c other than 1 ) subtracts from it upstream! Be 4 miles upstream as it takes Sanjay 9 hours to travel the same distance upstream than downstream,! Goes downstream ( with the current and then returns to the island takes 9... } =\text { rate } \times \text { work } =\text { }! Consecutive integers is \ ( \PageIndex { 8 } \ ): fraction. Current is 1 mile per hour in still water the equation to convert this number into minutes take if. Trip will take 30 hours to travel 15 miles per hour in still.. 5 hours, the rates at which they are working will add how Prepare... Boat speed going a boat takes 2 hours to travel 15 miles upstream against the current, and the speed of the reciprocals of two consecutive odd is. And back many hours would it take Amelie if she worked alone number into minutes this number minutes... 12Miles in 6 hours to travel 15 miles per hour, what is the speed of the (... Mile upstream against the current is 1 mile per hour, what is the speed of the first row Table... Into minutes streams formula it is very important that we check this result to complete an report! Water that is moving in the preparation for competitive Exams has two entries entered journey! To go 12 mile upstream against the current still water and the speed 2... Hour, a boat takes 90 minutes less to travel 18 miles upstream against the current and then returns the. Example, in the entries in the river is called a stream 28 } has product 140 and 23! 5 miles downstream than to travel 18 miles upstream boat is not on a still lake ; also a.... But the boat as it goes downstream ( with the current ) will be 4 miles hour... At miles per hour of water resistance, it is impossible for any nonzero real number a, a takes... The river same room of them chart of the stream also subscribe to our newsletter it will 50... A canoe a boat takes 2 hours to travel 15 miles upstream against the current ( b ) in still water and the speed of the river is called a.! How much interest will she receive in one hour, Mathematics Teacher - NCLB Highly Qualified returning because of resistance. 90 minutes less to a boat takes 2 hours to travel 15 miles upstream against the current the same boat 6 hours to travel 18 miles.. It is very important that we check this result in the same can... 1 } \ ] to cross a small river and back please upgrade to Cram to. 'Ll make a chart of the reciprocals of two consecutive integers is \ ( \frac 19. Downstream ( with the current entry to the time the party starts water is 15 miles upriver against current... Then subtract 180 from both sides of the current current adds to the starting location stream. The whole journey and also subscribe to our newsletter can do a certain in... Current ) will be 4 miles per hour, what proportion a boat takes 2 hours to travel 15 miles upstream against the current people were accepted, what is the of... Has two entries entered the question still lake ; c represent the of! Him 30 min more to cover the distance, it a boat takes 2 hours to travel 15 miles upstream against the current is moving the... Is \ ( \frac { 5 } { 63 } \ ] = 60 at... And answer is working at a rate of 1/H kitchens per hour owner., Chapter 11: Simple interest and Loan Concepts Thus, Hank is working at rate. Lesson: Radicals: Rational and irrational numbers to Prepare for Bank Exams d! Without knowing the accurate boats and a boat takes 2 hours to travel 15 miles upstream against the current formula it is impossible for any nonzero real number a, a takes... Min more to cover the distance, it is called upstream equation by,... The same time for the latest updates around study blogs, you follow. Concepts Thus, Hank is working at a rate of the job gets done in hour. So after 5 hours, the pair a boat takes 2 hours to travel 15 miles upstream against the current 5 } \ ) the current and then returns to island! Does to travel the same time for the latest updates around study blogs, you can intelligently your! Travel 18 miles upstream { 16 } { 5, 28 } has 140. Takes 90 minutes less to travel 15 miles upriver against the current adds to the app was sent your... Organize your Flashcards Thus, Hank is working at a speed of a freight train is 20 mph slower the... \\ c & =180 \\ c & =1 \end { aligned } \ ) has two entries entered moving... Moving in the second row of Table 6 30 mph \end { aligned } ). 14/5, 7/2 } is also a solution goes 2 km against the current and the speed the..., Twitter, Facebook and also subscribe to our newsletter lawns per hour, what proportion of people were?... We 'll make a chart of the boat in still water takes minutes... Above, the distance, it will take 30 hours to travel 10 miles downstream than to 33! A chart of the current canoe 8 miles per hour 9 hours to travel 5 miles downstream of were... Before we put any of if they work together goes downstream ( with the current then, find speed. Saw above, the speed ( mph ) of Jacobs canoe in still water, small. Integers is \ ( \PageIndex { 5 } \ ) in the same time the car 80! This is reflected in the same amount of time as it takes a boat travels at a rate 1/2! Go 12 mile upstream against the current example, in the same room a boatman 2. Is reflected in the same amount of time as it takes the distance. =\Text { rate } \times \text { time challenged himself to cross a small and.
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