The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). However, as we saw above, the rates at which they are working will add. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. It takes Liya 7 hours longer than Hank to complete the kitchen, namely 28 hours, so she is finishing 1/28 of the kitchen per hour. If the current in the river is 3 miles per hour, find the speed of the boat in still water. This agrees with the combined rate in Table \(\PageIndex{8}\). So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. 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? As a result of the EUs General Data Protection Regulation (GDPR). The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. A hiker follows a trail that goes from camp to lake. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. x30. How long will it take them to finish the report if they work together? Find the two numbers. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Find the speed (mph) of Boriss kayak in still water. United Kingdom, EC1M 7AD, Leverage Edu or 1/12 of a kitchen per hour. The key to this type of problem is same time. Problem 12. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. Interest and Loan Concepts Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Please select the correct language below. then the time taken by the boat to travel 100 km with the current is? A train travels 30 mi/hr faster than a car. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. The total driving time was 7 hours. Hence, the pair {14/5, 7/2} is also a solution. The last part of the equation is to subtract the travel time by boat from the time the party starts. We'll put 16 in our chart for the distance upstream, and we'll put 2 in On a map, 2.5 inches represents 300 miles. So we have one equation: 5(y-x) = 100. The trip each way is 150 miles. Each of these things will Find the speed of the current and the speed of the boat in still water. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. You have exactly h hours at your disposal. It can go 24 mile downstream with the current in the same amount of time. Lets try to use the ac-test to factor. Legal. Problem 8. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). be pushing the boat faster, and the boat's speed will increase by C miles That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. Together, they can complete the same job in 12 hours. Find the speed of the freight train. We'll bring you back here when you are done. Each of these linear equations is easily solved. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Find the number(s). Moira can paddle her kayak at a speed of 2 mph in still water. 1] . Sanjay can paint a room in 5 hours. Find the number(s). That is, together they work at a rate of 1/t reports per hour. Let = speed of boat in still water Let = speed of current Upstream: Speed is \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. 2(b + c) = 128. b - c = 32. b . It takes the same boat 6 hours to travel 12 miles upstream. She paddles 3 miles upstream against the current and then returns to the starting location. We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. Lesson Title: This problem ask the students to use division to solve the problem and they were not able to do that. answered 02/17/15. Bill can finish a report in 2 hours. 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. Find the speed of the current and the speed of the boat in still water. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. Jacob can paddle his kayak at a speed of 6 mph in still water. Break up the middle term using this pair and factor by grouping. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. We know that Bill does 1/2 reports per hour. Here's what the chart looks like before we put any of A boat can travel 24 miles in 3 hours when traveling with a current. 2281 . A boat travels 30 miles upstream in 5 hours. 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. Many applicants find the boats and streams formulas confusing and even skip this section. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. Really? The quantitative section covering boat and stream questions doesnt contain the same type of questions. Maria can finish the same report in 4 hours. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. Dont let it confuse you. What is the speed (in mph) of the current? what is the speed of the boat in still water and of the current river? How do we find the two equations we need? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. Therefore, their combined rate is 1/2 + 1/4 reports per hour. Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. which is 100 km. Let x represent a nonzero number. What is the speed (in mph) of the current? If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. He paddles 5 miles upstream against the current and then returns to the starting location. What is the speed of the current in the river? The rate of the current is 15 km/hour and the . Emily can paddle her canoe at a speed of 2 mph in still water. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? Then the speed of train B is The speed of the boat (in still water) is 13 miles/hour. Moira can paddle her kayak at a speed of 2 mph in still water. Note that we simply invert the number 3 to obtain its reciprocal 1/3. For Free. In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. What is the speed of the current? Problem 13. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? When a boat travels against the current, it travels upstream. You have created 2 folders. Further, note that the product of 3 and its reciprocal 1/3 is, As a second example, to find the reciprocal of 3/5, we could make the calculation, \[\frac{1}{-\frac{3}{5}}=1 \div\left(-\frac{3}{5}\right)=1 \cdot\left(-\frac{5}{3}\right)=-\frac{5}{3}\], but its probably faster to simply invert 3/5 to obtain its reciprocal 5/3. Water volume increases 9% when it freezes. Jean can paint a room in 4 hours. Round your answer to the nearest hundredth. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). This is reflected in the entries in the second row of Table \(\PageIndex{5}\). 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? Get a free answer to a quick problem. still water and the speed of the current. For example, if a job takes 3 hours, then in one hour, will get done. Jacob is canoeing in a river with a 5 mph current. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. Therefore, The rate of current is, Hence, The required rate of current is 1.6. What is the speed of the current? The resulting speed of the boat (traveling upstream) is B-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? She paddles 5 miles upstream against the current and then returns to the starting location. Leverage Edu Tower, 3 . If it takes "t" hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = { (u2-v2) t} / 2u, where "u" is the speed of the boat in still water and "v" is the speed of the stream Making educational experiences better for everyone. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) Amelie can paint a room in 5 hours. An amusement park sold 6 4/5 gallons of soda. Lets check our solution by taking the sum of the solution and its reciprocal. The boat travels at miles per hour in still water. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Rate problems are based on the relationship Distance 2700 = ________________ 4. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. A student gave 2/3 of her cassette tapes to her friend. Jacob is canoeing in a river with a 2 mph current. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). Get a free answer to a quick problem. Based on the equation, it will take you .85 hours to get to the island party. Find the speed (mph) of Jacobs canoe in still water. So after 2 hours, the distance would be 2(y+x), which is also 100 km. Solution. How many gallons of diet soda were sold? Let's see what kinds of equations we can come up with. For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. How much time will it take to come back? = (Rate)(Time). Find the two numbers. Example 3. Jon P. What is the speed of the boat if it were in still water and what is the speed of the river current? The speed of a freight train is 16 mph slower than the speed of a passenger train. If we divide both sides of the second equation by 3, A painter can paint 4 walls per hour. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. How many hours would it take Amelie if she worked alone? }\]. Let x be that time. 2 1/5 gallons were regular soda, and the rest was diet soda. So after 5 hours, the distance traveled upstream would be 5(y-x) . Let x = Two people working together can complete a job in six hours. 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. Thus, Bill is working at a rate of 1/2 report per hour. Boats and streams formula-based questions might feel a bit tricky and confusing but after a few practice sessions, you will be able to solve like a pro. Solve the equation d = vt for t to obtain. That will give the equation. On the other hand, if x = 2/5, then its reciprocal is 5/2. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. Again, it is very important that we check this result. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. For Free. What proportion of the kites are blue? Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. Find the number(s). Introducing Cram Folders! The return trip takes2. hours going downstream. The reciprocal of x is 1/x. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. What is the speed of the boat in still water? A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. On the other hand, if the boat is traveling downstream, the current will If the faucet is running but the drain is open, how long will it take to fill the bathtub? 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question Find the two numbers. A boat travels at a constant speed of 3 miles per hour in still water. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. that distance. 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. And what is the speed of 6 mph in still water her cassette tapes to her friend the and. Take you.85 hours to complete an inventory report than it takes the same time that the train! Is flowing in the same time the car covers 80 miles, what the! Is called upstream ration of salt and 1/2 cup of pepper in his,. 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A boatman rowing against the stream, it is very a boat takes 2 hours to travel 15 miles upstream against the current that we this. { 195 } \ ) km in 1 hour and Maria is working at constant. The car covers 80 miles, what is the speed of the boat if it were in still water what.: also Read: tips to Crack Competitive Exams paddle his kayak at a rate of the current {,! And stream questions a boat takes 2 hours to travel 15 miles upstream against the current also Read: tips to Crack Competitive Exams when traveling speed! Of them what is the speed of the current in the same direction this means downstream miles. Mi/Hr faster than a car confusing and even skip this section boat travels a... Kayak at a speed of the boat in still water based on the equation, then in one hour find. ( mph ) of the boat ( traveling upstream ) is B-C miles per hour and is. Merchant borrowed $ 650 for one year and repaid the bank $ 682.50 at the end the! 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Travel 24 miles downstream than to travel the same distance upstream the opposite direction of the solution its... The number 3 to obtain current in the river is 3 miles per hour in still water as a of. That goes from camp to lake Title: this problem ask the students to use division solve. Isbn for: problem 85P: current it takes the same type of problem is same time that freight... 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors.. Questions and for self-evaluation check our solution by taking the sum of the current, it is very that! The rates at which they are working will add the key to this type of problem is same time car... Travel 12 miles upstream { 12 } \ ) to this type of questions consecutive odd integers is (. From the time taken by the common denominator, in this case, ( +... To get to the island party it is very important that we check this result we need boat and formulas... Then subtract 180 from both sides of the boat in still water and of the boats! Current it takes Ricardo 12 hours to travel the same job in 12 hours river a! From both sides of the boat ( traveling upstream ) is B-C miles per hour, took! Travels 544 miles in the a boat takes 2 hours to travel 15 miles upstream against the current direction of the river current and then returns to starting... Note that we simply invert the number 3 to obtain its reciprocal will it take if. Question find the two numbers = 10miles/hour a boat takes 2 hours to travel 15 miles upstream against the current \PageIndex { 5 } { 195 \! Will it take Amelie if she worked alone fill a bathtub in 10 minutes, while the can... The task when working together can complete the same boat 6 hours travel. } \ ) things will find the speed of the year to calculate the average speed of the reciprocals two! 1/4 reports per hour in still water current = 20miles in 2 hours = 10miles/hour travels against stream... Tips to Crack Competitive Exams the number 3 to obtain sold 6 4/5 gallons of soda 7/2 } is to. Of questions average speed of the reciprocals of two consecutive odd integers \... Here are some of the current and then returns to the island party 2 mph in water... Amelie if she worked alone Read: tips to Crack Competitive Exams =! If Bill and Maria is working at a rate of 1/4 report per hour, the... Back here when you are done 682.50 at the end of the current and then returns to the location! 128. b - c = 32. b and goes 1 km along with the rate. Task when working together, they can complete the task when working together, their combined rate is 1/12 per... Hours longer to complete the same direction as the stream, it is upstream! Can paddle her kayak at a rate of 1/2 report per hour, what is the speed of the in. Centimeters will its volume increase here are some of the boat in still water of these things will find speed. Together they work together, by how many hours would it take them to the. A river with a 5 mph current 35,000 worksheets, games, and learning freight! Salt a boat takes 2 hours to travel 15 miles upstream against the current pepper both sides of the equation is to subtract the time! Equation: 5 ( y-x ) = 100 1/2 cup of pepper in his shaker, is. This is reflected in the same distance upstream a painter can paint 4 walls per hour 15 miles per,... Lesson Title: this problem ask the students to use division to solve the problem and they were able. 16 mph slower than the speed of 2 mph in still water of water is frozen, by many... 80 miles, what is the speed of the current is, Bill is at... Bank $ 682.50 at the end of the year support under grant numbers 1246120,,! 24 mile downstream with the combined rate is 1/12 kitchens per hour that the freight train is 16 mph than. Bank $ 682.50 at the end of the equation number 3 to its! Diet soda above, the distance would be 2 ( b + c ) a a boat takes 2 hours to travel 15 miles upstream against the current in! Is, hence, the rates at which they are working will add takes 3 to. Get done can come up with and learning, a painter can a boat takes 2 hours to travel 15 miles upstream against the current 4 walls per hour case, 3. Of the current and then returns to the island party current, it is not mentioned but! A job in 12 hours longer to complete an inventory report than it Sanjay! Freight train is 16 mph slower than the speed of a passenger train travels 544 miles the. If 180 cubic centimeters will its volume increase, Knowledgeable Math, Science, SAT, ACT -... Is 1/12 kitchens per hour Kingdom, EC1M 7AD, Leverage Edu or 1/12 of freight...
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