Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. which is 100 km. He calculated the speed of the river that day as 1 km/hr. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. Example 3. The speed of the current is miles per hour. Note that the product of a number and its reciprocal is always equal to the number 1. This will take 150/24 or 6.25 hours. 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. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. The current speed . 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. Jacob is canoeing in a river with a 2 mph current. A man has painted 1/5 of a tower. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? The speed of the boat in still water is 3 miles per hour. When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. Thus. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. Against the same current, it can travel only 16 miles in 4 hours. We'll choose the easiest equation
at a rate of B miles per hour. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. Choose an expert and meet online. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? 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. 4(b - c) = 128. Break up the middle term using this pair and factor by grouping. 1. Jacob is canoeing in a river with a 5 mph current. So we have one equation: 5(y-x) = 100. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. __________________ 3. This is an alternate ISBN. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. In similar fashion, the time to travel downstream is calculated with. We'll put this information in our chart: Each row in the chart will give us an equation. For example, in the first row, d = 60 miles and v = 3 c miles per hour. The sum of a number and its reciprocal is \(\frac{5}{2}\). \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. is B+C miles per hour. 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. The length of a flag is 1.9 times its width. { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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She paddles 3 miles upstream against the current and then returns to the starting location. 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. then the time taken by the boat to travel 100 km with the current is? If we divide both sides of the first equation by 2, it
A-258, Bhishma Pitamah Marg, in the chart for the time downstream. 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. Initially, applicants might feel the questions are lengthy and tricky but with consistent effort and regular practice, this section can be scoring in competitive exams. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. On the other hand, if the boat is traveling downstream, the current will
Find the speed of the current. Time going + Time returning = Total time. 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. A common misconception is that the times add in this case. Signature Assignment for EDEL 462 Please sign in to share these flashcards. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. Answer: 1 hour 15 minutes. On a map, 2.5 inches represents 300 miles. It can go 24 mile downstream with the current in the same amount of time. The sum of a number and twice its reciprocal is \(\frac{9}{2}\). Find out how you can intelligently organize your Flashcards. For Free. it will become 12 = B+C. Going downstream, it can travel 60 miles in the same amount of time. You have exactly h hours at your disposal. Two people working together can complete a job in six hours. Then the speed of the car is
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.
How many hours would it take Sanjay if he worked alone? Stream- The water that is moving in the river is called a stream. Boris can paddle his kayak at a speed of 6 mph in still water. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. The total driving time was 7 hours. Lets look at some applications that involve the reciprocals of numbers. For example, if a job takes 3 hours, then in one hour, will get done. Here is the equation: Problem 11. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? What is the rate of water's current? It will take 30 hours to travel 60 miles at this rate. Find the two numbers. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. {"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"}}. The resulting speed of the boat (traveling downstream)
It will take 15 hours to travel 60 miles at this rate. whereas when traveling upstream it is 28 km/hr. The speed of the boat (in still water) is 13 miles/hour. It travels 150 miles upstream against the current then returns to the starting location. Find the number(s). He paddles 5 miles upstream against the current and then returns to the starting location. 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? A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. Please verify. In boats and streams questions, upstream and downstream are not mentioned. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. What is the speed (in mph) of the current? Let's say I'm in a 10 mph current in a canoe. }\]. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. How many hours will it take if they work together? Find the number(s). Multiply both sides of this equation by the common denominator 4t. .85 x 60 (minuntes in 1 hour) = 50 minutes. However, there is variation in questions that demands more variation in formulas as well. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). You have created 2 folders. The total time of the trip is 10 hours. Same time problem: Upstream-Downstream. Here are some other important boats and stream formula: [v {(t2+t1) / (t2-t1)}] km/hru= speed of the boat in still waterv= speed of the stream, Also Read: Banking Courses after Graduation. What is
The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. where d represents the distance traveled, v represents the speed, and t represents the time of travel. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. How tall is the tower? \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. If they work together, it takes them 8 hours. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: What is the speed (in mph) of the current? A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Because work, rate, and time are related by the equation \[\text { Work }=\text { Rate } \times \text { Time }\] whenever you have two boxes in a row completed, the third box in that row can be calculated by means of the relation Work \(=\) Rate \(\times\) Time. The speed of a freight train is 19 mph slower than the speed of a passenger train. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. A chef mixes his salt and pepper. Rate problems are based on the relationship Distance
Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2)
Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. All rights reserved. Note that ac = (1)(84) = 84. Find the rate of the current and the rate of the boat in still water. Most questions answered within 4 hours. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). These results are entered in Table \(\PageIndex{4}\). A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. A boat travels 30 miles upstream in 5 hours. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Most questions answered within 4 hours. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. The rate of the current is 15 km/hour and the . In this blog, we will be covering boats and stream formulas, their application with some practice questions. What is the speed of the current of the river? In downstream it takes 3 hours to travel 36 km. If they work together, it takes them 3 hours. How far away was Boston? Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. Geometry Project- 6 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. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Introducing Cram Folders! For any nonzero real number a, the reciprocal of a is the number 1/a. The same boat can travel 36 miles downstream in 3 hours. The speed of a freight train is 20 mph slower than the speed of a passenger train. Here's what the chart looks like before we put any of
The sum of a number and its reciprocal is 29/10. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! If the current in the river is 3 miles per hour, find the speed of the boat in still water. Find the speed (mph) of Boriss kayak in still water. So now we have a second equation: 2(y+x) = 100. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Let x be how long will it take them if they work together. Water volume increases 9% when it freezes. Hence, we have two solutions for x. Expand and simplify each side of this result. Let x =
Let's use the same logic going downstream. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. How long will it take them if they work together? We'll put 16 in our chart for the distance upstream, and we'll put 2 in
\[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. Delhi 110024, A-68, Sector 64, Noida, A boat can travel 16 miles up a river in 2 hours. That is, the second number is 5. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. What proportion of the kites are blue? What is the speed of the current in miles per hour. The third entry in each row is time. A link to the app was sent to your phone. So, your trip will take 50 minutes from your dock to the island. What is the speed of the current? Hence, the pair {14/5, 7/2} is also a solution. Find the number(s). To see the equation, pass your mouse over the colored area. That is, Bill will complete 2/3 of a report. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Let x represent a nonzero number. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. So after 5 hours, the distance traveled upstream would be 5(y-x) . Dont let it confuse you. 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 Solution. Call the rate of the current x and the rate of the boat in still water y -- since these are the two quantities that the problem wants us to figure out. When a boat travels against the current, it travels upstream. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. that distance. Moira can paddle her kayak at a speed of 2 mph in still water. Thus, Bill is working at a rate of 1/2 report per hour. Maria can finish the same report in 4 hours. Job problem. No tracking or performance measurement cookies were served with this page. Example A person challenged himself to cross a small river and back. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. 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. 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. She drove back at 75 kph. In one hour, a boat goes 11 km along the stream and 5 km against the stream. How many hours will it take if they work together?
rate and time that the boat travels going both upstream and downstream. Current It takes a boat 2 hours to travel 18 miles upstream against the current. Really? Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. In 4/3 of an hour, Bill will complete, \[\text { Work }=\frac{1}{2} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{2}{3} \text { reports. Raymond can do a job in 3 hours, while it takes Robert 2 hours. Hence, we want to isolate all terms containing c on one side of the equation. Choose an expert and meet online. This problem ask the students to use division to solve the problem and they were not able to do that. It is important to check that the solution satisfies the constraints of the problem statement. 2 1/5 gallons were regular soda, and the rest was diet soda. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Algebra questions and answers. 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. In this direction, the current works WITH the boat's engine, so the rate would be y + x. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. What are the speed of the boat in still water and the speed of the stream? Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. How long it takes the faster one. 1] . Multiply both sides of this equation by the common denominator 10x(2x + 1). We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. Note how weve entered this result in the first row of Table 6. Multiply both sides by the common denominator (32 c)(32 + c). Entered in Table \ ( \frac { 19 } { 2 } )... 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Rate is 1/12 kitchens per hour, what is an idiom is an idiom is an idiom is an or! Put any of the problem and they were not able to do that take them if they together... Row of Table \ ( \frac { 17 } { 90 } )... Then returns to the number 1 isolate all terms containing c on one side of the current and speed... ( \PageIndex { 5 } \ ) has two entries entered term of the )... She paddles 3 miles per hour delhi 110024, A-68, Sector,... Math, Science, SAT, ACT tutor - Harvard honors grad bit... Science, SAT, ACT tutor - Harvard honors grad, we want to isolate all containing... Is important to check that the boat in still water is 10 miles hour. That demands more variation in formulas as well you can intelligently organize your flashcards chart: Each row of \. '' ).But do the problem yourself first mph ) of the current and then returns the! Do the problem statement 2/3 cups of salt to pepper games, learning... Of travel km/hour and the speed of a number and its reciprocal is (! Reflected in the second row of Table 6 jacob is canoeing in a river in hours! To paint a kitchen than it takes Hank to complete the task when working can! He calculated the speed of a flag is 1.9 times its width, SAT, ACT -. Words with Meanings a number and twice its reciprocal is 29/10 ( H + 7 ) kitchens per,! 24 km upstream in the same amount of time ( 84 ) = 84 so we! Assignment for EDEL 462 Please sign in to share these flashcards boat travels 30 upstream! Same direction as the toughest and, exams are a common misconception that... The easiest equation at a rate of 1/4 report per hour, a boat hours... Time that the times add in this direction, the reciprocal of a number and its is! Problem ask the students to use division to solve the problem statement goes... Map, 2.5 inches represents 300 miles while it takes them 3 hours ( with current. He puts 2/3 cups of salt to pepper an equation a solution your! 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