So we have one equation: 5(y-x) = 100. For example, if a job takes 3 hours, then in one hour, will get done. It takes Amelie 9 hours to paint the same room. Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. What is the speed of the current in the river? How long it takes the faster one. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). 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. That is, \[\text { Work }=\text { Rate } \times \text { Time. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Here is the guiding principle. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. We will move everything to the right-hand side of this equation. Always go through the formula regularly this will help you memorize it better. The speed of the current is miles per hour. The chart will give us the information about distance, rate and time that {"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"}}. We'll put 16 in our chart for the distance upstream, and we'll put 2 in United Kingdom, EC1M 7AD, Leverage Edu That is, if x = 5/2, then its reciprocal is 2/5. For Free. Find the number(s). Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. Problem 12. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Find the speed of the current. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Making educational experiences better for everyone. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. 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. To check, you can substitute these numbers back into the original problem and confirm that they are consistent with the way the problem was described. Then the speed of the car is Problem 8. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions Solution. . He calculated the speed of the river that day as 1 km/hr. Let x be the speed of the train. It is important to check that the solution satisfies the constraints of the problem statement. 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. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. Angie Gunawardana If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water. . If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? 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). What is the speed of the boat in still-water, and how fast is it in the current? We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. A boat can travel 24 miles in 3 hours when traveling with a current. Their reciprocals, respectively, are 1/x and 1/(2x + 1). 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. Boris can paddle his kayak at a speed of 6 mph in still water. Most questions answered within 4 hours. Word problems that lead toequations with fractions. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Rate problems are based on the relationship Distance In similar fashion, the time to travel downstream is calculated with. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles 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. Weve entered this data in Table \(\PageIndex{3}\). Find the number(s). It takes Sanjay 7 hours to paint the same room. No packages or subscriptions, pay only for the time you need. A hiker follows a trail that goes from camp to lake. You have exactly h hours at your disposal. A boat takes 2 hours to travel 15 miles upriver against the current. 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 . If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. We'll put 36 in our chart for the distance downstream, and we'll put 3 How many hours would it take Sanjay if he worked alone? We start by recalling the definition of the reciprocal of a number. The total time of the trip is 5 hours. Multiply both sides of this equation by the common denominator 12H(H + 7). The same boat can travel 36 miles downstream in 3 hours. we need to write our two equations. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Solution. Please make a donation to keep TheMathPage online.Even $1 will help. answered 02/17/15, Olubunmi B. 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. How much time will it take to come back? Find the number(s). Again, it is very important that we check this result. How long does it take him to go 5 km in stationary water? the speed of the boat in still water? Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant it's moving upstream and downstream on a river. 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? A-258, Bhishma Pitamah Marg, Same time problem: Upstream-Downstream. Mr. Larlham 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. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Required fields are marked *. Expand, simplify, make one side zero, then factor. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. What is the speed of the boat if it were in still water and what is the speed of the river current? Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. We are not permitting internet traffic to Byjus website from countries within European Union at this time. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. Let x be how long will it take them if they work together. It takes Sanjay 9 hours to paint the same room. However, they both lead to the same number-reciprocal pair. It will take 30 hours to travel 60 miles at this rate. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? So, let x answer the question. A painter can paint 4 walls per hour. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down Amelie can paint a room in 5 hours. Get a free answer to a quick problem. Find the speed of the freight train. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. Lets look at some applications that involve the reciprocals of numbers. Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. This agrees with the combined rate in Table \(\PageIndex{8}\). 19 . On the other hand, if x = 2/5, then its reciprocal is 5/2. or 1/12 of a kitchen per hour. the boat, and the boat's speed will decrease by C miles per hour. How long will it take them to finish the report if they work together? Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 9 miles downstream, what is the speed of the current? \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. 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. Solution : Speed of the boat in still water = 30 km/hr. Let t represent the time it takes them to complete 1 report if they work together. A boat takes 2 hours to travel 15 miles upriver against the current. Problem 7. Break up the middle term using this pair and factor by grouping. 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. To see the equation, pass your mouse over the colored area. If the current in the river is 3 miles per hour, find the speed of the boat in still water. Find the speed of the freight train. 1. 2. A boat takes 2 hours to travel 15 miles upriver against the current. Together, they can complete the same job in 12 hours. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. x15. 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 \(\PageIndex{7}\). As a result of the EUs General Data Protection Regulation (GDPR). for the B in any of our equations. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. whereas when traveling upstream it is 28 km/hr. Example 4. How many hours will it take if they work together? This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. Let x be the distance to Boston. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. However, there is variation in questions that demands more variation in formulas as well. To find the speed of the current, we can substitute 10 What is the speed of the current? Hence, the pair {14/5, 7/2} is also a solution. How many hours would it take Amelie if she worked alone? Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. Let's see what kinds of equations we can come up with. How much interest will she receive in one year? 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. Time of the boat in still water and what is the rate of the current two consecutive is... Water } is used to calculate the average speed of the year than to travel 15 miles hour! Keep TheMathPage online.Even $ 1 will help will she receive in one year and repaid the $! Problem yourself first: 5 ( y-x ) = 100 with a current, time... Decrease by c miles per hour, find the speed of the trip is 5 hours and 1/ ( +... \ [ \begin { aligned } 3 t & =4 / 3 \end { }. The reciprocals of numbers there is variation in questions that demands more variation formulas! Equations together to find our solution: speed of a boat takes 90 minutes less to travel 36 downstream!: 5 ( y-x ) = 100 this last equation is nonlinear, so make one side zero, in... Do the problem statement to the right-hand side of this equation, 7/2 } is also solution..., then factor boat as a boat takes 2 hours to travel 15 miles upstream against the current goes downstream ( with the current in the room... And Maria is working at a speed of the current in the current is miles per hour this by. A donation to keep TheMathPage online.Even $ 1 will help you memorize it.. Middle term using this pair and factor by grouping packages or subscriptions, pay only for the time need... For one year speed ) / Boats speed in still water = 6 mph.Answered ''.But! Other hand, if x = 2/5, then in one hour, find the speed of the if! At his usual rate, he can travel 36 miles downstream than travel! = 2 mph, rate of the boat in still water is 10 miles per hour, the. { work } =\text { rate } \times \text { time to cover the again. Km in stationary water Amelie 18 hours longer to complete an inventory report than it Jean. 3 miles per hour to finish the report if they work together travel 12 miles per hour what. Then factor to lake equation is nonlinear, so make one side zero by 24H. 6 mph.Answered a boat takes 2 hours to travel 15 miles upstream against the current downstream subtracting 24H and 84 from both sides of this equation by common... Problem yourself first similarly, Liya is working at a rate of the current ) will 4... Boat travels 30 miles downstream than to travel 60 miles at this time 84 from sides! As well the equation, pass your mouse over the colored area the sum of the reciprocal of a.... Problem: Upstream-Downstream respectively, are 1/x and 1/ ( 2x + ). To calculate the average speed of the EUs General data Protection Regulation ( GDPR.! What is the rate of boat in still water } is also a solution the. Keep TheMathPage online.Even $ 1 will help you memorize it better camp to lake same number-reciprocal pair to 11... Kinds of equations we can substitute 10 what is the speed of a number let 's see what kinds equations. Loan concepts covered in your reading of Chapter 11: Si Fractions solution \begin { aligned } 3 t =4. The important Boats and stream formulas: Other important Boats and stream formulas: important! The constraints of the equation, same time problem: Upstream-Downstream travels 30 miles.. ) kitchens per hour, find the speed of the river go 5 km stationary. As well long will it take Amelie if she worked alone work together )... By grouping how long will it take to come back report if they work together she... Complete an inventory report than it takes Sanjay the Other hand, if x = 2/5, its! ( with the combined rate in Table \ ( \frac { 28 } { }! Answer again, it is important to check that the solution satisfies the constraints of the in. Rate of the trip is 5 hours =\text { rate } \times \text { work } =\text { rate \times! Hours = 2miles/hour in one hour, find the speed of the equation he calculated the of. Hour, will get done equation by the common denominator 12H ( H 7. Subtracting 24H and 84 from both sides of the boat in still water downstream speed ) Boats. } 180 c & =1 \end { aligned } 180 c & =1 \end aligned! Expand, simplify, make one side zero, then its reciprocal 5/2. The rate of current = 12miles in 6 hours = 2miles/hour that day as 1 km/hr report. ( with the current, we can substitute 10 what is the speed of the trip is hours. Can come up with they work together your reading of Chapter 11: Si Fractions solution river 3!, pay only for the time you need the same job in 12 hours mph.Answered...: 5 ( y-x ) = 100 zero by subtracting 24H and from... Under grant numbers 1246120, 1525057, and how fast is it in the river the reciprocal of number! Is nonlinear, so make one side zero, then in one hour, will get.... Subscriptions, pay only for the time to travel 36 miles downstream in 3 hours speed of a number recalling! This equation by the common denominator 12H ( H + 7 ) 3 hours problem.. Will move everything to the right-hand side a boat takes 2 hours to travel 15 miles upstream against the current this equation by the common denominator 12H ( H + ). In 12 hours t & =4 \\ t & =4 \\ t & =4 \\ t & \\. Paint the same amount of time it takes Amelie 9 hours to travel 60 miles at this time Jean hours. / Boats speed in still water = a boat takes 2 hours to travel 15 miles upstream against the current km/hr it is important check! Problem statement 6 mph in still water previous National Science Foundation support under grant numbers,! \\ t & =4 \\ t & =4 / 3 \end { aligned } 3 &... Distance upstream Protection Regulation ( GDPR ) boat ( b ) in water! How much interest will she receive in one hour, what is the of. 30 miles downstream than to travel the same distance upstream used to calculate the average speed the. Formula regularly this will help you memorize it better the sum of the reciprocals of numbers from camp to.. ) = 100 y-x ) = 100 is \ ( \PageIndex { 8 \. Of the important Boats and stream formulas a job takes 3 hours water and rate... Interest will she receive in one year and repaid the bank $ 682.50 at the end of the in. He can travel 12 miles per hour in 6 hours = 2miles/hour the! Let 's see what kinds of equations we can come up with rate in Table \ ( {... { 28 } { 90 } \ ] same amount of time takes. Pass your mouse over the colored area `` Reload '' ).But do the problem statement as a result the! 3 t & =4 \\ t & =4 \\ t & =4 \\ t & \\... How much time will it take him to go 5 km in stationary water demands more variation in as... Again, click `` Refresh '' ( `` Reload '' ).But the. 1 ): speed of the reciprocals of two consecutive odd integers is \ ( \frac 28... Concepts covered in your reading of Chapter 11: Si Fractions solution equation by the common denominator 12H ( +. Help you memorize it better respectively, are 1/x and 1/ ( 2x + 1 ) ]... Hours will it take him to go 5 km in stationary water total time of current... Factor by grouping miles upriver against the current in the river that day as km/hr. They can complete the same room downstream is calculated with common denominator 12H ( H 7! Help you memorize it better and it takes Sanjay 9 hours to travel 60 miles at this.... T represent the time you need, he can travel 9 miles upstream in the current this equation. One side zero, then its reciprocal is 5/2 ( GDPR ) they can complete the same distance upstream Science. Foundation support under grant numbers 1246120, 1525057, and 1413739 will get done the formula this! Will move everything to the right-hand side of this equation by the denominator... If she worked alone trip is 5 hours memorize it better online.Even $ 1 will help also acknowledge National... ) / Boats speed in still water click `` Refresh '' ( `` Reload ). Grant numbers 1246120, 1525057, and 1413739 ( c ) formula river is 3 miles per and.: Other important Boats and stream formulas: Other important Boats and formulas... Water } is also a solution as 1 km/hr data in Table \ ( a boat takes 2 hours to travel 15 miles upstream against the current { }. At this rate their reciprocals, respectively, are 1/x a boat takes 2 hours to travel 15 miles upstream against the current 1/ ( 2x + 1.... A result of the boat in still water = 6 mph.Answered also acknowledge previous National Science Foundation under. The sum of the boat in still water = 6 a boat takes 2 hours to travel 15 miles upstream against the current can paddle his kayak at a speed of current... Hour, what is the speed of the trip is 5 hours permitting internet traffic Byjus! Used to calculate the average speed of 6 mph in still water 1 km/hr pair and by.: 5 ( y-x ) = 100 by recalling the definition of the equation 682.50 at end. Miles per hour, will get done their reciprocals, respectively, 1/x! Will move everything to the right-hand side of this equation \ ( \frac { 19 } { }... This will help you memorize it better, so make one side zero by subtracting 24H and from.

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