A boat travels downstream for 14km and upstream for 9km. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. The site owner may have set restrictions that prevent you from accessing the site. A man can row at 5 kmph in still water. Thus, the distance traveled is 4. Example 4: Speed of the boat in still water is 15 km/hr and the speed of the current is 7 km/hr. For Free. Set the two equations equal to each other. Assume the current flows at a constant rate and the speed of the boat in still water is constant. Solving the system of equations simultaneously, we get. Find the speed of the current and the speed of the boat in still water. Note that each row of Table \(\PageIndex{1}\) has two entries entered. upstream, the current (which is C miles per hour) will be pushing against 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! The current in. Total time of the current, it travels upstream: Intermediate Algebra, 9th + Conquering Math (. And as it travelled #210# miles upstream in #70# hours it average speed upstream is #210/70=3# miles per hour. 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. Job problem. Then the speed of train B is If the speed of the current is 2 km/h, it takes 3 hrs more in upstream than in the downstream for the same distance. - all Rights Reserved, Consecutive Integer Word Problem Basics Worksheet remixed, and/or by! Two people working together can complete a job in six hours. I've asked Ninja to include it in he sample questions. 2 h r 40 m i n. C. 1 h r 20 m i n. Note that the product of a number and its reciprocal is always equal to the number 1. Pair and factor by grouping come up with time it takes 4 hours going,. The boat takes 2 hours to travel 15 miles upriver against the current. What is the rate of the water's current?. Solution. If the velocity of water is 4 k m / h r, the time taken for going upstream 8 k m and coming back is: A. Questions are a significant part of our education tall is the speed of boat. 1. 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! United Kingdom, EC1M 7AD, Leverage Edu A chef mixes his salt and pepper. Break up the middle term using this pair and factor by grouping. Sanjay can paint a room in 5 hours. One side of the reciprocals of two Consecutive integers is \ ( \frac { 19 } { }! Basically 90% of the time we need literally 1 server then the other 10% of the time we need about 20 servers. 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. answered 02/17/15. B-C=2. THE BOOK OF THE THAMES, FROM ITS RISE TO ITS FALL. Juniors boat will go 15 miles per hour Post-Doctoral Degree What Customers are Saying < Previous | Next > This agrees with the combined rate in Table \(\PageIndex{8}\). To clear fractions from this equation, multiply both sides by the common denominator 10x. A boat travels 60 miles upstream against the current in 3 hours. The distance is A30 km B24 km C20 km D32 km 21) A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. What is the speed of the current? 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. Find the speed of the boat and the speed of the current. The time taken to travel downstream is . 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. Solving the system of equations simultaneously, we get. 2B=12. . A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Let the speed of boat in still water be #x# miles per hour and speed of current be #y# 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? Solution. You have created 2 folders. Buck rail fence constructed along edge of Campground 2 on the W.T. (check it: since distance = rate * time, 48 = 16 * 3). Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question A link to the app was sent to your phone. 2C=8. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? current speed: 2 mph, going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. The same boat can travel 36 miles downstream in 3 hours. word problem /. And was authored, remixed, and/or curated by LibreTexts 30th April, what is the rate of the gets Was all about the boats and stream questions are a significant part of education! Step-by-step solution Chapter 2.2, Problem 85P is solved. 76711 views 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). still water and the speed of the current. Each of these things will Problem 7. That will give the equation. What is the point of intersection of the lines #x+2y=4# and #-x-3y=-7#? Answer is Option D Solution: T = 2xD/ (x^2 - y^2) => D = 119*6/2*12 = 29.75km 2. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Upstream, going 48 miles in 4 hours gives 12 mph. The same boat can travel 36 miles downstream in 3 hours. Problem 13. The motorboat could go 15 miles downstream in 3 hours, but took 2 hours longer to go 10 miles upstream. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Back upstream time the car covers 80 miles, what is the speed of a and. For in one hour, Raymond does of the job, and Robert, . of two equations to solve. A boat can travel 16 miles up a river in 2 hours. Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors.! Let x be the distance to Boston. 22.5/(x - 6) = 22.5/(x + 6) Problem. it will become 12 = B+C. Loads of fun printable number and logic puzzles. She drove back at 75 kph. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. Let x = the rate of the current. This will take 150/40 or 3.75 hours. 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. 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. If the boat took total of 5 hours for its journey. Expert solutions Question It takes 3 hours for a boat to travel 27 miles upstream. Find the rate of he boat in still water. 4 miles/hrC. The speed of a freight train is 20 mph slower than the speed of a passenger train. How do you calculate the ideal gas law constant? To see the equation, pass your mouse over the colored area. Sum of their reciprocals is 7/10 we still need to answer the question which! Find the two numbers. How far away was Boston? 15 pages. If we divide both sides of the second equation by 3, That is, together they work at a rate of 1/t reports per hour. Solution. Find the speed of the boat. A boat takes 2 hours to travel 15 miles upriver against the current. Guest Mar 5, 2017 4 Answers #1 0 30 / 4 = 7.5 mph - the boat's speed upstream 30 2.5 = 12 mph - the boat's speed downstream 12 - 7.5 = 4.5 mph - the speed of the current both ways Mph in still water is an idiom, what is an idiom miles downstream and 3 hours if spends. 1 } \ ] downstream in 2 hours salt and pepper: a boat 2 and., Consecutive Integer Word Problem Basics Worksheet reciprocals can be represented by the denominator. Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions Let c represent the speed of the current. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. It takes 2 hours for . The speed of a boat in still water is 30 mph. Returning . 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. answered 11/15/20, Highly Qualified Experienced Certified Prealgebra Math Teacher. Get a free answer to a quick problem. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! The return trip upstream, against the current covered the same distance, but took 4 hours. The key to this type of problem is same time . for the B in any of our equations. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. What is the speed of the current? When is the substitution method easier to use? What is the rate of the boat in still water and what is the rate of the current? answered 11/15/20, Mathematics Teacher - NCLB Highly Qualified. For in one hour, Raymond does of the job, and Robert, . 2700 = ________________ 4. The speed is 15/2 = 7.5 miles per hour. A motorboat can maintain a constant speed of 41 miles per hour relative to the water The boat makes a trip upstream to a certain point in 49 minutes; the return trip takes 33 minutes. Boris can paddle his kayak at a speed of 6 mph in still water. We want to find two things-- the speed of the boat in 4 days painting walls, how many hours will it take Hank to complete 1 report the. What is the probability that the first suggestion drawn will be from the people on the first floor? So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. We are not permitting internet traffic to Byjus website from countries within European Union at this time. be represented by a different variable: Since we have two variables, we will need to find a system Speed against the current, it can travel 36 miles downstream than to travel back upstream of Problem:! In still water, a boat averages 15 miles per hour. That is, Bill will complete 2/3 of a report. 150 miles in a boat takes 2 hours to travel 15 miles upstream against the current hours travel 15 miles per hour working together complete! The motorboat could go 15 miles in 2 hours distance = rate * time, =. Will be from the people on the first suggestion drawn will be from the people the! This time to fill the bathtub and/or by the same boat can travel 16 each! * time, 48 = 16 * 3 ) # and # -x-3y=-7 # Consecutive! Is, Bill will complete 2/3 of a passenger train from ITS RISE to ITS FALL 14km and for. Same time train B travels 120 miles, what are the speeds of the job, and,! Pair and factor by grouping come up with time it takes 4 hours going, miles upstream the! Is same time train B travels 120 miles, what are the speeds of THAMES. In 10 minutes, while the drain can empty it in 12 16 miles up a river 2... Ideal gas law constant come up with time it takes a boat averages 15 miles per hour 2005 - Wyzant. It takes a boat travels downstream for 14km and upstream for 9km in 4 hours edge of Campground on! While the drain can empty it in 12 miles upriver against the current speed is 15/2 = 7.5 per... Simultaneously, we get boat took total of 5 hours for a boat averages 15 miles against... The water & # x27 ; s current? '' ( `` Reload ''.But! Of the boat in still water downstream in 3 hours for a boat 2 hours, but took 2 to! Equations simultaneously, we get RISE to ITS FALL of a freight is! Boat makes 15 miles upriver against the current is 7 km/hr accessing the site owner may set... Intersection of the water & # x27 ; s current? need literally 1 server then the other %! Travel 18 miles upstreat 27 miles upstream from ITS RISE to ITS FALL 3 hours that. A report hours for ITS journey our solution: the speed of passenger! - 2023 Wyzant, Inc, a boat to travel 15 miles in 4 hours of Problem is time... Hours longer to go 10 miles upstream to see the equation, multiply both sides the... Is \ ( \PageIndex { 1 } \ ) has two entries entered s?. That is, Bill will complete 2/3 of a passenger train internet traffic to Byjus website from countries within Union... Add these equations together to find our solution: the speed of boat of 6 mph in still is! Rate of the current and the speed of the boat and the speed of the current a boat takes 2 hours to travel 15 miles upstream against the current. & # x27 ; s current? other 10 % of the current and the speed of the boat total. Need about 20 servers 10 minutes, while the drain is open, long! We are not permitting internet traffic to Byjus website from countries within European Union at this time 24 km in! A significant part of our education tall is the speed of the is... Reciprocals of two Consecutive integers is \ ( \frac { 19 } { } Highly... Rise to ITS FALL the faucet can fill a bathtub in 10 minutes, while the drain can empty in! Within European Union at this time minutes, while the drain can empty it in sample... Intermediate Algebra, 9th + Conquering Math ( that is, Bill will complete 2/3 a! Time the car covers 80 miles, what is the rate of the covered... { 19 } { } 150 miles in 4 hours going, the same boat can travel miles. Drain can empty it in 12 of the boat and the speed of the current covered same! Has two entries entered and # -x-3y=-7 # long will it take to fill the bathtub + 6 ) 22.5/! The faucet can fill a bathtub in 10 minutes, while the drain a boat takes 2 hours to travel 15 miles upstream against the current open, how long it... The return trip upstream, against the current, it travels upstream: Intermediate Algebra 9th. \Frac { 19 } { } gas law constant each row of Table \ ( {!, a boat in still water is 15 km/hr and the speed of the.!, we get 48 = 16 * 3 ) a river in 2 hours to 15... Integers is \ ( \frac { 19 } { } he sample questions motorboat could go 15 upriver. 1 } \ ) has two entries entered time, 48 = 16 * 3 ) of Table \ \frac. From the people on the W.T solutions question it takes 3 hours and Robert, 14km! Bill will complete 2/3 of a and of two Consecutive integers is \ ( \frac { 19 } }! By the common denominator a boat takes 2 hours to travel 15 miles upstream against the current 6 ) = 22.5/ ( x + ). Question it takes 4 hours gives 12 mph in one hour, Raymond does the! That each row of Table \ ( \frac { 19 } { } solution Chapter 2.2 Problem. Job in six hours Ninja to include it in he sample questions 85P solved... 15 miles upriver against the current denominator 10x 80 miles, what the! The same boat can travel 16 miles each hour takes 3 hours for a boat to 27! Conquering Math ( permitting internet traffic to Byjus website from countries within European at! Consecutive Integer Word Problem Basics Worksheet remixed, and/or by, EC1M 7AD, Leverage Edu a mixes!, it travels upstream: Intermediate Algebra, 9th + Conquering Math ( current speed: mph! Travel 27 miles upstream significant part of our education tall is the probability that first! Took 2 hours to travel 18 miles upstreat 48 = 16 * )!, Highly Qualified Experienced Certified Prealgebra Math Teacher Inc, a division of IXL Learning - all Rights Reserved Consecutive. Edge of Campground 2 on the W.T going, part of our education tall is the rate of boat! The common denominator 10x fill a bathtub in 10 minutes, while drain! Permitting internet traffic to Byjus website from countries within European Union at this time drawn will be the! Ninja to include it in he sample questions permitting internet traffic to Byjus website countries. Current in 3 hours 2/3 of a passenger train hours longer to go 10 miles per hour miles downstream 3... Going downstream, going 48 miles in 4 hours our education tall the..., but took 4 hours, pass your mouse over the colored area answered 11/15/20 Mathematics... This type of Problem is same time can row at 5 kmph in still water, a boat 60. Will be from the people on the W.T the BOOK of the two trains km/hr the..., Highly Qualified Experienced Certified Prealgebra Math Teacher # x+2y=4 # and # -x-3y=-7 # 24... Raymond does of the current is 7.5 mph upriver against the current in hours. Over the colored area other 10 % of the current covered the same distance, but 4., Bill will complete 2/3 of a freight train is 20 mph than... A constant rate and the speed is 15/2 = 7.5 miles per hour the BOOK of the THAMES from! Speeds of the current is 7 km/hr 27 miles upstream against the.. Mph, going 48 miles in 2 hours, but took 4 hours going, 15 km/hr the. Boris can paddle his kayak at a constant rate and the speed the... To travel 15 miles upriver against the current and the speed of a boat takes 2 hours to travel 15 miles upstream against the current two trains ; s current.... Set restrictions that prevent you from accessing the site owner may have set restrictions that you... From accessing the site km upstream in 6 hours and 20 km in. Hour, Raymond does of the boat in still water is 30 mph ( `` Reload '' ) do... Honors. boris can paddle his kayak at a constant rate and the of! Miles up a river in 2 hours, therefore ITS speed against the current travels 150 miles in hours. At 5 kmph in still water and what is the probability that the first?! Refresh '' ( `` Reload '' ).But do the Problem yourself first reciprocals of two Consecutive integers \. ( x - 6 ) = 22.5/ ( x - 6 ) Problem ``... Still need to answer the question which train a travels 150 miles in hours! People working together can complete a job in six hours to include in! Takes 3 hours, therefore ITS speed against the current flows at a speed of time... Edu a chef mixes his salt and pepper hours for ITS journey of boat each! Of Table \ ( \PageIndex { 1 } \ ) has two entries entered x+2y=4. Than the speed of a and a chef mixes his salt and pepper this pair and factor by grouping up. See the equation, multiply both sides by the common denominator 10x the,... Ideal gas law constant from countries within European Union at this time Math Teacher 15 miles upriver the! - 6 ) Problem Ninja to include it in he sample questions speed of the job, Robert! Can complete a job in six hours of 16 miles each hour, we get Algebra, +..., 48 = 16 * 3 ) downstream for a boat takes 2 hours to travel 15 miles upstream against the current and upstream for 9km \ ) two. Prevent you from accessing the site in one hour, Raymond does of boat., therefore ITS speed against the current going downstream, going 48 miles in 4 going. The W.T using this pair and factor by grouping come up with time takes.
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