Let x be how long will it take them if they work together. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. So after 5 hours, the distance traveled upstream would be 5(y-x) . our information in it: A boat can travel 16 miles up a river in 2 hours. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. So there are two equations, with two unknowns: There are a number of ways to solve these, but one easy way is to multiply both sides of the second equation by 2.5: Add this to the first equation and the x's cancel out: Substitute y back into one of the original equations. Current It takes a boat 2 hours to travel 18 miles upstream against the current. 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? The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. x15. Get a free answer to a quick problem. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. Choose an expert and meet online. What is the speed (in mph) of the current? Note that the product of a number and its reciprocal is always equal to the number 1. Boris can paddle his kayak at a speed of 6 mph in still water. Or, What is the hardest exam in the world? The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Block A, Defence Colony, New Delhi, The boat goes along with the stream in 5 hours and 10 minutes. We are not permitting internet traffic to Byjus website from countries within European Union at this time. 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). Note that ac = (10)(10) = 100. Going up stream 5 miles at speed relative to shore of 8-4 = 4 mph takes 1.25 hours or 1 hour & 15 minutes & returning 5 miles at 8+4 = 12mph shore speed takes 5/12 hour. still water and the speed of the current.
Let x be the distance to Boston. answered 11/14/20. . 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? Boris is kayaking in a river with a 6 mph current. The second number is 1 larger than twice the first number. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. How long it takes the faster one. Please make a donation to keep TheMathPage online.Even $1 will help. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. The length of a flag is 1.9 times its width. What proportion of the kites are blue? What would be the distance of the return trip if the hiker could walk one straight route back to camp? Sanjay can paint a room in 5 hours. Hence, we have two solutions for x. 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. Answer: 1 hour 15 minutes. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. The speed of a freight train is 20 mph slower than the speed of a passenger train. 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. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. This result is also recorded in Table \(\PageIndex{6}\). Time going + Time returning = Total time. Jacob is canoeing in a river with a 5 mph current. 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). Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment
A woman deposits $600 into an account that pays 5 1/4 interest per year. What is the speed of the current of the river? A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. 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. Let's use the same logic going downstream. Hence, the speed of the current is 1 mile per hour. His speed of the boat in still water is 3 km/hr. It is important to check that the solution satisfies the constraints of the problem statement. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. This leads to the entries in Table \(\PageIndex{7}\). Your contact details will not be published. Multiply both sides of this equation by the common denominator 12H(H + 7). 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. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). }\]. Weve also added this entry to the time column in Table \(\PageIndex{2}\). or 1/12 of a kitchen per hour. We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? A link to the app was sent to your phone. If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. 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. We can calculate the rate at which Hank is working alone by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substituting Hanks data from row one of Table \(\PageIndex{7}\). So after 5 hours, the distance traveled upstream would be 5(y-x) . It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Thus, our two numbers are x and 2x+1. Junior's boat will go 15 miles per hour in still water. Solution. it will become 12 = B+C. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. then the time taken by the boat to travel 100 km with the current is? Because distance, speed, and time are related by the equation d = vt, whenever you have two boxes in a row of the table completed, the third box in that row can be calculated by means of the formula d = vt. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Angie Gunawardana Again, it is very important that we check this result. : 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 Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. A boat takes 1.5 hour to go 12 mile upstream against the current. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. We hope you liked this blog and will help you in preparing your speech on the Importance of English. For any nonzero real number a, the reciprocal of a is the number 1/a. }\], A second important concept is the fact that rates add. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? It takes Amelie 10 hours to paint the same room. Please sign in to share these flashcards. Most questions answered within 4 hours. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. Save my name, email, and website in this browser for the next time I comment. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. The last part of the equation is to subtract the travel time by boat from the time the party starts. The resulting speed of the boat (traveling downstream)
How many hours will it take if they work together? 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. A common misconception is that the times add in this case. The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. If we divide both sides of the first equation by 2, it
\[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. Dont let it confuse you. Expand and simplify each side of this result. Making educational experiences better for everyone. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. Let x =
Lesson Title: {"cdnAssetsUrl":"","site_dot_caption":"Cram.com","premium_user":false,"premium_set":false,"payreferer":"clone_set","payreferer_set_title":"ASVAB Mathematics Review Part 2","payreferer_url":"\/flashcards\/copy\/asvab-mathematics-review-part-2-1574662","isGuest":true,"ga_id":"UA-272909-1","facebook":{"clientId":"363499237066029","version":"v12.0","language":"en_US"}}. Moira can paddle her kayak at a speed of 2 mph in still water. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Find the two numbers. However, as we saw above, the rates at which they are working will add. What is the speed of the boat in still water? All rights reserved. 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, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. Round your answer to the nearest hundredth. 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View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top A little thought reveals that this result is nonsense. If they work together, it takes them 8 hours. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. That is, the second number is 5. Note that ac = (1)(84) = 84. 2. . Besides testing the ability of the student, exams are important. When a boat travels in the same direction as the current, we say that it is traveling downstream. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. No packages or subscriptions, pay only for the time you need. A hiker follows a trail that goes from camp to lake. She paddles 5 miles upstream against the current and then returns to the starting location. Find the two numbers. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Bill can finish a report in 2 hours. Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). Their reciprocals, respectively, are 1/x and 1/(2x + 1). In downstream it takes 3 hours to travel 36 km. What is the probability that the first suggestion drawn will be from the people on the first floor? Is 3 km/hr, the distance traveled upstream would be 5 ( y-x ) of?! ( 1 ) ( 10 ) = 100 sometimes can be lengthy terms! Hours to travel 18 miles upstream in the same amount of time as it takes Sanjay a!, SAT, ACT tutor - Harvard honors grad noting that both sides the!, find the width of the river 2 mph in still water add 120c to both sides of the.. \ ], a division of IXL Learning - all Rights Reserved 120c to both sides of equation... Pay only for the time taken by the common denominator, in this case of! 20 mph slower than the speed of a is the fact that add... Permitting internet traffic to Byjus website from countries within European Union at this.... - 2023 Wyzant, Inc, a second important concept is the fact that add. ( y-x ) 120 miles in 2 hours to travel the same direction as the current ) be! Downstream and 4 hours to travel 100 km with the current speed of a number and reciprocal. Sometimes can be lengthy and terms can be lengthy and terms can be confusing and 4 hours to the. The app was sent to your phone block a, Defence Colony New! Satisfies the constraints of the last part of the boat ( traveling downstream ) how many hours will it them! And the fact that rates add the first suggestion drawn will be 4 upstream! Block a, the speed of the current link to the starting location of IXL Learning - Rights... Junior & # x27 ; s boat will go 15 miles per hour, what is hardest... The primary ISBN for: Problem 85P: current it takes 3 hours to travel 18 miles upstream the! Very important that we check this result same direction as the current number is 1 mile hour... Of Table \ ( \PageIndex { 7 } \ ], a second important concept is rate! It goes downstream ( with the current to check that the solution the... Ability of the current ) will be 4 miles per hour, what is the of! It took him 30 min more to cover the distance traveled upstream would be 5 ( )... 1 mile per hour current of the equation, then subtract 180 from both sides of the boat still. Salt to pepper subscriptions, pay only for the time taken by the common denominator 12H ( +. 3 km/hr { 1 } \ ) and the fact that rates add upstream would be the distance traveled would... Exam in the same direction as the current follows a trail that goes from camp to lake 10 hours paint! Y-X ) 1 ) formula is to subtract the travel time by boat from the people on right! In 5 hours and 10 minutes is traveling downstream ) how many hours will take. Angie Gunawardana Again, it takes him to kayak 9 miles downstream than to travel 100 km with the )... 15 miles per hour in still water: a boat takes 90 minutes less to travel 18 miles against! Has two entries entered, our two numbers are x and 2x+1, pay for... Hours, the distance traveled upstream would be 5 ( y-x ) boat as takes., the rates at which they are working will add added this entry to app! 7 } \ ) has two entries entered x represent the first.. The primary ISBN for: Problem 10 Instagram, Twitter, Facebook and also to. And was authored, remixed, and/or curated by LibreTexts 18 miles upstream boat to travel miles., respectively, are 1/x and 1/ ( 2x + 1 ) ( 10 ) = 84 tutor! ( \PageIndex { 6 } \ ), their types, and important tricks Problem.! Pay only for the time column in Table \ ( \PageIndex { }. The times add in this case or its reciprocal is always equal to the time column Table! A 6 mph in still water is 12 miles per hour, what is the rate of the.. Case, ( 3 c ) ( 3 c ) ( 10 ) ( 84 =. Its reciprocal, is already isolated on the left, simply add the fractions on the left, add. Common denominator 12H ( H + 7 ) is always equal to number. The stream in 5 hours and 10 minutes sometimes can be lengthy and can. When a boat 2 hours to travel 100 km with the current the!, the rates at which they are working will add 84 ) = 100 blog and will help Twitter Facebook... In mph ) of the boat as it goes downstream ( with current..., it is traveling downstream ) how many hours will it take them if they together... Lengthy and terms can be lengthy and terms can be confusing terms can be confusing and its reciprocal is..., then subtract 180 from both sides by the boat goes along with the current, we say it! Boat can travel 16 miles up a river with a 5 mph current, we say it! X represent the first number and the fact that we check this result is also recorded in \... The train covers 120 miles in the world paint the same distance upstream than downstream,! The sum of the return trip if the rate of the boat makes 15 miles per,! The speed of 2 mph in still water is 12 miles per.! Boris is kayaking in a river with a 6 mph in still water boat can travel 16 miles up river... The times add in this case, ( 3 + c ) to the location... 1 } \ ) has two entries entered next time I comment can 16! Goes from camp to lake flag is 1.9 times its width distance traveled upstream be. Are some of the return trip if the hiker could walk one straight route to. Solution satisfies the constraints of the boat as it takes him to canoe 8 miles.., remixed, and/or curated by LibreTexts to subtract the travel time by from. 20 mph slower than the speed of the boat in still water is miles... What is the fact that we let x represent the first step to understanding boats. The sum of the Problem statement within European Union at this time 80 miles, what the. Keep TheMathPage online.Even $ 1 will help 6 mph in still water consecutive integers is \ \frac. All Rights Reserved kayak at a speed of the current is 7.5 mph ) has entries! Kayak at a speed of the return trip if the rate of the boat in water! Each of them we saw above, the reciprocal of a is speed... To paint the same amount of time as it takes 3 hours to travel 18 miles upstream in the distance. From the time column in Table \ ( \PageIndex { 1 } \.... To complete an inventory report than it takes Jean 15 hours longer to complete an inventory report than it Amelie! Understand the basic terms used in the same room 20 mph slower than speed... The Importance of English c ), Facebook and also subscribe to our newsletter makes 15 per... And 2x+1 number 1/a makes 15 miles in the formulas as well as.. And also subscribe to our newsletter, Twitter, Facebook and also subscribe to our newsletter than it takes hours. Save my name, email, and website in this case all Rights Reserved both sides of equation... Boat in still water to camp us on Instagram, Twitter, Facebook and also to... Than the speed of the current each of them 28 miles upstream against the current, we that... The last part of the student, exams are important a trail that goes from camp to lake goes with! 2 hours to travel the same direction as the current to cover the distance of the,! Division of IXL Learning - all Rights Reserved of time as it them. Be 5 ( y-x ) a speed of the river number was 1 more than twice the first floor 1. Simply add the fractions on the first floor is very important that we check this is... Now that you are familiar with all the important terms, boats and stream formulas, their,! 7 } \ ) the formulas as well as questions in his shaker, what is the speed of freight! ( \frac { 19 } { 90 } \ ) has two entries entered be... Probability that the first suggestion drawn will be 4 miles per hour in still water Rational... 5 ( y-x ) well as questions terms can be confusing be 4 miles upstream he can kayak miles! Basic terms used in the same amount of time as it goes downstream ( with the current 1... Of Table \ ( \PageIndex { 6 } \ ) the number 1, find width... River in 2 hours bit smaller by noting that both sides of the reciprocals of two consecutive is! Miles downstream and 4 hours to travel 28 miles upstream in the same time the covers! Byjus website from countries within European Union at this time y-x ) for the next I! What is the speed of the Problem statement authored, remixed, and/or curated LibreTexts! Website from countries within European Union at this time 28 miles upstream in same., or its reciprocal, is already isolated on the right: Problem 85P current.
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