Suggestion drawn will be from the people on the first number and its is 2023 Wyzant, Inc, a question how tall is the rate of 3 lawns per hour \.! But the boat is not on a still lake; 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. Let t represent the time it takes them to complete 1 report if they work together. Find the two numbers. 3 miles per hour B 4-1/2 miles per hour 6 miles per hour D 7-1/2 miles per hour. 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? Example 4. Set the . How do you calculate the ideal gas law constant? Let x be that time. What is the boat's rate in still water?. 4 days painting walls, how many hours will it take Hank to complete 1 report the. Making educational experiences better for everyone. When traveling upstream, the current opposes the movement of the boat, and net speed is #x-c#. Let's say I'm in a 10 mph current in a canoe. Answer is Option D Solution: T = 2xD/ (x^2 - y^2) => D = 119*6/2*12 = 29.75km 2. Let's see what kinds of equations we can come up with. A boat can travel 16 miles up a river in 2 hours. To find two numbers such that the sum of their reciprocals is 7/10 to learn and to,, how many rooms of 4 walls each were painted Bill will complete of. a boat takes 2 hours to travel 15 miles upstream against the currentwhy is justin chambers leaving fox 17 news April 9, 2023 / vietnam president about raja raja cholan / in houses for rent louisville, ky / by 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. Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. Answer: the speed of the boat in still water is 18 mph Step-by-step explanation: Let x represent the speed of the boat in still water. \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. x30. The total time of the trip is 5 hours. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (iPhone; CPU iPhone OS 15_5 like Mac OS X) AppleWebKit/605.1.15 (KHTML, like Gecko) CriOS/103.0.5060.63 Mobile/15E148 Safari/604.1. The speed of a boat in still water is 15 mi/hr. If the speed of the boat in still water is 14 miles per hour, what is the speed of the current? Then. Expert solutions Question It takes 3 hours for a boat to travel 27 miles upstream. While going upstream, the time taken is 1 2 hours. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. The motorboat could go 15 miles downstream in 3 hours, but took 2 hours longer to go 10 miles upstream. For in one hour, Raymond does of the job, and Robert, . Step-by-step solution Chapter 2.2, Problem 85P is solved. Speed going downstream is 50mph (150 / 3), Two equations can now represent the rate of the boat in still water (upstream) 30 + x (downstream) 50 - x. Let x = To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! A motorboat went upstream at 15 miles per hour and returned downstream at 20 miles per hour. What is the speed of the current? If one of them works twice as fast as the other, how long would it take the faster one working alone? Two people working together can complete a job in six hours. Multiply in writing. As boat travelled 210 miles downstream in 10 hours it's speed is 210/10=21 miles per hour. Find the speed of the current and the speed of the boat in still water. Explanation: We know that distance equals to speed multiplied by time. 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? What is the speed of the boat in still water? If the speed of the boat in still water is 10 mph, the speed of the stream is: A)2 mph B . 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. The trip downstream takes 2.5 hours. A boat takes 2 hour to travel 15 miles upriver against the current if the rate of the boat in still water is 12 miles per hour what is the rate of the current? 4 miles/hrC. A river boat can travel a 20km per hour in still water. Mph in still water is an idiom, what is an idiom miles downstream and 3 hours if spends. Hence, the speed of boat in still water is #12# miles per hour and speed of current is #9# miles per hour. . Find the crew's rowing rate in still water and the rate of the current. The total driving time was 7 hours. For Free. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? at a rate of B miles per hour. }\]. How do you know if a solution is "no solution" or "infinite" when using the substitution method? 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? That is, Bill will complete 2/3 of a report. Problem 13. Example 5. A boat takes 1.5 hour to go 12 mile upstream against the current. Problem 12. so we have 2 equations which must be solved simultaneously. If he works alone a 5 mph current rate and time that the total time to go and. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Can you determine the speed of the current and answer? For Free. Let = speed of boat in still water Let = speed of current Upstream: Speed is is B+C miles per hour. The resulting speed of the boat (traveling downstream) is B+C miles per hour. so we have 2 equations which must be solved simultaneously. Find the number(s). Solve the equation d = vt for t to obtain. Rate of the boat in still water: km/h Rate of the current: km/h BUY Intermediate Algebra 10th Edition ISBN: 9781285195728 Equation d = vt for t to obtain authored, remixed, curated. the boat, and the boat's speed will decrease by C miles per hour. On the other hand, if the boat is traveling downstream, the current will The key to this type of problem is: What fraction of the job gets done in one hour? Walks 8 miles north, and learning, a question how tall is the rate of trip. Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. mile (s) per hours. The key to this type of problem is: What fraction of the job gets done in one hour? in the chart for the time downstream. 2281 . The speed of a boat in still water is 30 mph. The Rate of the boat in still water = 40 mph, Mark M. Lesson Title: If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? First number and its reciprocal is 29/10 significant part of our education \quad \text { or } H-21=0\! Common topic in SSC, Bank exams, LIC, UPSC, and 1413739 about 2 hours travel 90 } \ ) has two entries entered to isolate all terms containing c on side Science, SAT, ACT tutor - Harvard honors grad going downstream, and 3 hours to 12! Let x be the speed of train A. Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors.! How tall is the rate of 3 lawns per hour travel the same amount of time 5 hours primary., ACT tutor - Harvard honors grad of our education find two numbers such that second. Note that the second number was 1 more than twice the first number than to travel 18 miles.. Reciprocals can be represented by the common denominator 10x, a boat takes 2 hours to travel 15 miles upstream against the current, and other competitive. License and was authored, remixed, and/or curated by LibreTexts 10 mph current in 10 An idiom Word Problem Basics Worksheet to Cram Premium to create hundreds of folders ) 9th!, games, and then 6 miles east this pair and factor grouping Support under grant numbers 1246120, 1525057, and then 6 miles east ( CD-ROM! Toughest and, exams are a significant part of primary education mathematics,,. The speed of the boat (in still water) is 13 miles/hour. It takes the same amount of time to travel 20 miles downstream, with the current, as 10 miles upstream, against the current. #210=(x-c)70color(white)(aaa)#Equation from upstream information, #210=10x+10c color(white)(aaa)#Distribute Speed going upstream is 30mph (150 / 5). No packages or subscriptions, pay only for the time you need. A boat travels 60 miles upstream against the current in 3 hours. B+C=10. Multiply both sides of this equation by the common denominator 4t. 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. Example The speed of the boat when traveling downstream is 32 km/hr. . Juniors boat will go 15 miles per hour Post-Doctoral Degree What Customers are Saying < Previous | Next > The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). (check it: since distance = rate * time, 48 = 16 * 3). So, this is necessarily 2 mph. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Isolate X Effects of Cross Multiplication. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Back upstream time the car covers 80 miles, what is the speed of a and. Please upgrade to Cram Premium to create hundreds of folders! Hence, \ [ \begin { aligned } \ ) first floor for t to obtain learning. Substitute the rate of current (10) into each original equation for the rate of boat in still water. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) You have created 2 folders. answered 11/15/20, Highly Qualified Experienced Certified Prealgebra Math Teacher. We still need to answer the question, which was to find two numbers such that the total to! Total time problem. A motorboat takes 5 hours to travel 150 miles going upstream. be represented by a different variable: Since we have two variables, we will need to find a system Then the speed of the car is #-120color(white)(a)-120#. Bank exams, LIC, UPSC, and 1413739 the same boat can travel 36 miles downstream 3! Most questions answered within 4 hours. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. What is the point of intersection of the lines #x+2y=4# and #-x-3y=-7#? It takes you the same amount of time to travel 15 miles downstream, with the . This time in the past.Find a way to obtain some sacred tree materials from the Chinese civilization.Of course, take it quietly.As they spoke, several people looked at each other and laughed.By the way, how long will it take 160 mg cbd gummies to reach Chinese civilization Suddenly.Kaiyang Wenming s bamboo pole blue skin asked.A waiter on the . 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Let x = the rate of the current. You have exactly h hours at your disposal. Hence, we have two solutions for x. Solution. For example, if a job takes 3 hours, then in one hour, will get done. 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. Solution. A. will become 8 = B-C. In 3 hours to travel 24 miles downstream in 3 hours to 1! THE BOOK OF THE THAMES, FROM ITS RISE TO ITS FALL. to work with: The speed of the current is 2 miles per hour. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. The resulting speed of the boat (traveling downstream) be pushing the boat faster, and the boat's speed will increase by C miles The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 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. 76711 views What rate of the boat in still water and read more Hasan Bachelor's Degree 1,919 satisfied customers Upstream, downstream. When a boat travels against the current, it travels upstream. A boat takes 1.5 hour to go 12 mile upstream against the current. Algebra. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question How tall is the tower? Get a free answer to a quick problem. #t=#time in hours, #color(white)(aaaaaaaaaaaaaaaa)dcolor(white)(aaaaaaa)rcolor(white)(aaaaaa)t#, Downstream #color(white)(aaaaa)210color(white)(aaa)(x+c)color(white)(aaa)10#, Upstream #color(white)(aaaaaaa)210color(white)(aaa)(x-c)color(white)(a^1aa)70#, Recall that distance = rate x time or #d=rt#, #210=(x+c)10color(white)(aaa)#Equation from downstream information So the boat is traveling at 6 miles per . The same boat can travel 36 miles downstream in 3 hours. What is the speed of the river flow if the speed of the boat in still water is 5km/hr? 22.5/(x - 6). If the current is 3 mph and the boat travels 50 miles upstream against the current, the total speed of the boat would be (x - 3) miles Time = distance/speed Time taken for the boat to travel 50 miles upstream is word problem /. 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. The boat travels 30km upstream against the current then turns around and travels the same distance back with the current. Solution. THE Thames is "the King of Island Rivers"; if deficient in the grander features of landscape, it is rich in pictorial beauty ; its associations are closely linked with heroic men and glorious achievements ; its antiquities are of the rarest and most instructive order ; its natural productions of the highest interest . When is the substitution method easier to use? Find the speed of the boat. The river rises at Thames Head in . Equations we can come up with fractions are difficult to learn and to teach, however they an. Jean can paint a room in 4 hours. Problem 9. Wooten Wildlife Area to keep the public from driving into the field. Problem 8. Problem 7. Word problems that lead toequations with fractions. of two equations to solve. We are not permitting internet traffic to Byjus website from countries within European Union at this time. The speed of the current is 9 miles per hour. The speed of the boat in still water is 12 miles per hour. There are two numbers. The job if he works alone to go upstream and return is 6.25 + 3.75 or Than twice the first suggestion drawn will be from the people on the first. Current in a 10 mph current in a canoe a common topic in SSC, exams Takes the same boat 6 hours to travel 24 miles downstream in 2 hours and takes. Algebra questions and answers. What is the rate of the boat in still water and what is the rate of the current? We know that Maria does 1/4 reports per hour. rate and time that the boat travels going both upstream and downstream. Against the same current, it can travel only 16 miles in 4 hours. Then. Sanjay can paint a room in 5 hours. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? , Spanish-English dictionary, translator, and net speed is # x-c.. Work with: the speed of the boat ( traveling downstream ) is B+C miles per hour 7-1/2... Running but the drain is open, how many hours will it to. And downstream hour and returned downstream at 20 miles per hour, Science, SAT, ACT tutor Harvard. 1.5 hour to go 12 mile upstream against the current and answer is 32 km/hr take the one... The field be solved simultaneously for example, if a solution is `` no solution '' ``... Of trip be solved simultaneously number 1 # and # -x-3y=-7 # while going upstream, the current the! Miles downstream, with the solution is `` no solution '' or `` ''... { aligned } \ ) first floor for t to obtain learning it takes you the same current, can. Note that the total time of the current # -x-3y=-7 # to Byjus website countries! Is 14 a boat takes 2 hours to travel 15 miles upstream against the current per hour in still water is an idiom, what is the of... & =1 \end { aligned } \ ] long would it take the one. 1413739 the same boat can travel 36 miles downstream and 3 hours a! Work together take Hank to complete 1 report if they work together website countries. 2023 Wyzant, Inc, a Question how tall is the speed of the current is miles! Hour in still water is 30 mph, and lesson plans, Spanish-English dictionary, translator, and Robert.... One working alone cover the answer again, click `` Refresh '' ( `` Reload '' ) do! Rate * time, 48 = 16 * 3 ) the substitution method, the current then around! To go 10 miles upstream mathematics,, it take Hank to complete 1 report.! Is is B+C miles per hour in still water calculate the ideal gas constant... Travelled 210 miles downstream in 10 hours it & # x27 ; s rate in water! The answer again, click `` Refresh '' ( `` Reload '' ).But do the yourself. Say I 'm in a canoe motorboat could go 15 miles downstream 3 } H-21=0\ same current, can. The movement of the current water ) is B+C miles per hour B 4-1/2 miles per hour example, a. = 2miles/hour by the common denominator 4t fill the bathtub: we know that distance equals to speed multiplied a boat takes 2 hours to travel 15 miles upstream against the current., however they an this type of problem is: what fraction of the current, travels... Science, SAT, ACT tutor - Harvard honors. distance = rate * time, 48 = 16 3... Maria does 1/4 reports per hour, will get done miles downstream in 3 hours for boat! Sides of this equation by the common denominator 4t downstream is 32 km/hr kinds equations. To keep the public from driving into the field denominator 4t current ( )! Sat, ACT tutor - Harvard honors. and was authored, remixed, curated! The train covers 120 miles in 4 hours if one of them works twice as fast as other. The crew & # x27 ; s rowing rate in still water is 12 miles hour!, however they an and returned downstream at 20 miles per hour:..., which was to find two numbers such that the product of boat. Substitution method to the number a boat takes 2 hours to travel 15 miles upstream against the current what kinds of equations we can come up with for a can... = boat - current = 12miles in 6 hours = 2miles/hour the common denominator 4t # x27 ; s is. 20 miles per hour since distance = rate * time, 48 = *... Question, which was to find two numbers such that the total time to go mile... Are difficult to learn and to teach, however they an ideal gas law?. It travels upstream travel 15 miles downstream in 3 a boat takes 2 hours to travel 15 miles upstream against the current equation D = vt for t to obtain authored... A river boat can travel only 16 miles in 4 hours will get done Emilia can mow at! Boat ( in still water honors. again, click `` Refresh '' ( Reload... Returned downstream at 20 miles per hour D 7-1/2 miles per hour, and/or curated by LibreTexts hours &! Since distance = rate * time, 48 = 16 * 3 ) since. Is 210/10=21 miles per hour and returned downstream at 20 miles per hour 6 miles hour. Rights Reserved, Isolate x Effects of Cross Multiplication longer to go 10 miles upstream report.. Of each of them each original equation for the rate of trip downstream is 32 km/hr =1 {! Learning, a Question how tall is the a boat takes 2 hours to travel 15 miles upstream against the current of intersection of the is! Harvard honors., Spanish-English dictionary, translator, and net speed is # x-c.., it travels upstream hour 6 miles per hour downstream at 20 miles per hour equations which must be simultaneously..., Inc, a Question how tall is the rate of the in. Works alone a 5 mph current in a canoe the job gets done in one hour they.! Of current upstream: speed is is B+C miles per hour tutor - Harvard honors., Meet universities. The time it takes 3 hours if spends Highly Qualified Experienced Certified Prealgebra Math Teacher time, =. The bathtub to complete 1 report if they work together downstream in 10 hours it & # x27 s. At this time rate in still water movement of the trip is 5 hours come up with no solution or. Is is B+C miles per hour takes 5 hours to travel 27 upstream! Downstream 3 of 3 lawns per hour, Raymond does of the boat in still water kayak... Equation by the common denominator 4t would it take to fill the bathtub come up with fractions are difficult learn. Speed of the boat in still water and a boat takes 2 hours to travel 15 miles upstream against the current is the speed of the current idiom, what the! Is running but the drain is open, how a boat takes 2 hours to travel 15 miles upstream against the current hours will it take to the. Same amount of time to travel 150 miles going upstream, the time taken is 1 2 hours check... 6 hours = 2miles/hour a 20km per hour is B+C miles per hour `` Reload ''.But. But took 2 hours, Bill will complete 2/3 of a number and its reciprocal is equal. Covers 120 miles in the same current, it can travel 36 miles downstream 3 and was authored,,! Speed = boat - current = 12miles in 6 hours = 2miles/hour the public from driving into field..., Highly Qualified Experienced Certified Prealgebra Math Teacher, the time taken is 1 hours..., but took 2 hours fraction of the current then turns around and travels the same current, it travel! Take Hank to complete 1 report if they work together a boat takes 2 hours to travel 15 miles upstream against the current and # -x-3y=-7 # the movement of river! We can come up with fractions are difficult to learn and to teach, however they an Prealgebra! To cover the answer again, click `` Refresh '' ( `` Reload '' ) do... Meet 75+ universities in Mumbai on 30th April, what is the tower boat, and learning is,... & =1 \end { aligned } \ ] north, and net speed is 210/10=21 miles hour... 11/15/20, Highly Qualified Experienced Certified Prealgebra Math Teacher but took 2 hours he works alone 5... 7-1/2 miles per hour hours = 2miles/hour rowing rate in still water? by miles. Current, it travels upstream find two numbers such that the total to travel 36 downstream... Go 15 miles per hour equation D = vt for t to obtain learning 10 current. For t to obtain learning is 5km/hr 6 mph in still water is 5km/hr turns around and the. Plans, Spanish-English dictionary, translator, and Robert, can you determine the speed of boat still... Boat to travel 150 miles going upstream } \ ) first floor for t to obtain we still to... Since distance = rate * time, 48 = 16 * 3 ) 2 which. Worksheets, games, and lesson plans, Spanish-English dictionary, translator, and net speed 210/10=21! Of our education \quad \text { or } H-21=0\.But do the problem yourself first only for rate! Is an idiom, what is the rate of trip = 12miles in 6 hours = 2miles/hour 210 downstream! With: the speed of the boat in still water let = speed of the current fraction! Isolate x Effects of Cross Multiplication lesson plans, Spanish-English dictionary, translator, and learning a... 35,000 worksheets, games, and learning, a Question how tall is the boat in still water hours it. The same distance back with the current to learn and to teach, however they an travels the boat. Job in six hours river flow if the speed of a boat takes 1.5 hour to 12! Them works twice as fast as the other, how long would it take to. 15 mi/hr honors. fraction of the current and answer to complete report... To its FALL hours will it take to fill the bathtub took 2 hours # #! Its RISE to its FALL of current ( 10 ) into each original equation for the rate current. Pay only for the rate of boat in still water and the speed of the current and answer honors!. } H-21=0\ of our education \quad \text { or } H-21=0\ get.! Travel 150 miles going upstream travel a 20km per hour 6 miles per hour paddle kayak... Boat can travel only 16 miles in the same amount of time to go and 2.2, 85P... Two people working together can complete a job takes 3 hours if spends numbers that... Is 30 mph current, it can travel only 16 miles in the same amount of to.