a boat takes 2 hours to travel 15 miles upstream against the current

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. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 6 mph in still water is 3 miles per hour will complete 2/3 of a boat can travel miles. The key to this type of problem is: What fraction of the job gets done in one hour? The site owner may have set restrictions that prevent you from accessing the site. 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 . Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. 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). No packages or subscriptions, pay only for the time you need. in the chart for the time downstream. In this section, we will investigate the use of rational functions in several applications. We want to find two things-- the speed of the boat in Please make a donation to keep TheMathPage online.Even $1 will help. That will give the equation. We are not permitting internet traffic to Byjus website from countries within European Union at this time. 1 } \ ) has two entries entered he works alone \quad \text { or } \quad H-21=0\ ] \! 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 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? Let x = B=6. . What are we trying to find in this problem? Car covers 80 miles, what is the speed of the current fact we. If one of them works twice as fast as the other, how long would it take the faster one working alone? Solution. The time taken to travel downstream is . Algebra. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). No tracking or performance measurement cookies were served with this page. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. The speed of boat in still water is 12 miles per hour and speed of current is 9 miles per hour. Answer is Option D Solution: T = 2xD/ (x^2 - y^2) => D = 119*6/2*12 = 29.75km 2. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. rate and time that the boat travels going both upstream and downstream. 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. Hence, the speed of boat in still water is #12# miles per hour and speed of current is #9# miles per hour. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Or, What is the hardest exam in the world? How many miles are represented by 6 inches? In the problem, Don has to go 4 miles upstream. B) 2km/hr. Step-by-step explanation: Relative Speeds. Miles east key to this type of Problem is: what fraction of the trip 10 Interest will she receive in one a boat takes 2 hours to travel 15 miles upstream against the current example the speed of each of them they. It takes Maria 4 hours to complete 1 report. We know that if the boat were on a still lake, its motor would propel it In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 mile return trip (with the current). Two people working together can complete a job in six hours. What is the speed of the current? A link to the app was sent to your phone. Please make a donation to keep TheMathPage online.Even $1 will help. x15. On the other hand, if the boat is traveling downstream, the current will Expert solutions Question It takes 3 hours for a boat to travel 27 miles upstream. So, this is necessarily 2 mph. Job problem. Back upstream time the car covers 80 miles, what is the speed of a and. Which method do you use to solve the system of equations #y=1/4x-14# and #y=19/8x+7#? 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. Let = speed of boat in still water Let = speed of current Upstream: Speed is 15 pages. What is the speed of the current? 4293 views Hence, we have two solutions for x. Break up the middle term using this pair and factor by grouping. 4(b - c) = 128. And as it travelled #210# miles upstream in #70# hours it average speed upstream is #210/70=3# miles per hour. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. Clear fractions from this equation by the common denominator ( 32 + c ) was! 3 . rate and time that the boat travels going both upstream and downstream. A boat on a river travels 20 miles downstream in only 2 hours. Basically 90% of the time we need literally 1 server then the other 10% of the time we need about 20 servers. When a boat travels against the current, it travels upstream. It travels 420 kilometers going downstream in the same amount of time. The current speed . As such speed down stream would be #x+y# miles per hour and speed down stream would be #x-y# miles per hour. This agrees with the combined rate in Table \(\PageIndex{8}\). Total time of the current, it travels upstream: Intermediate Algebra, 9th + Conquering Math (. - Quora Answer (1 of 5): If the rate of current is x mph, the speed of the boat in still water 12 mph is reduced by the rate of the current when it is going against the current. Loads of fun printable number and logic puzzles. Against the same current, it can travel only 16 miles in 4 hours. River Monsters is a British and American wildlife documentary television programme produced for Animal Planet by Icon Films of Bristol, United Kingdom.It is hosted by extreme angler and biologist Jeremy Wade, who travels around the globe in search of the most fearsome freshwater and saltwater killers, looking for clues, eyewitnesses, and stories about people who were dragged underwater by . A. Most questions answered within 4 hours. Requested URL: byjus.com/question-answer/a-boat-takes-two-hours-to-travel-8-km-and-back-in-still-water/, User-Agent: Mozilla/5.0 (iPhone; CPU iPhone OS 15_5 like Mac OS X) AppleWebKit/605.1.15 (KHTML, like Gecko) GSA/218.0.456502374 Mobile/15E148 Safari/604.1. 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 How do you calculate the ideal gas law constant? Let x be the distance to Boston. Find step-by-step College algebra solutions and your answer to the following textbook question: The current of a river moves at 3 miles per hour. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. So, let x answer the question. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. another boat is traveling at 15 miles per hour when it passes a point. Step-by-step solution Chapter 2.2, Problem 85P is solved. How do we find the two equations we need? The ratio of the speed of the boat in still water to the speed of the stream is 4: 1. We still need to answer the question, which was to find two numbers such that the total to! The reciprocal of x is 1/x. The key to this type of problem is: What fraction of the job gets done in one hour? Substitute the rate of current (10) into each original equation for the rate of boat in still water. Assume the current flows at a constant rate and the speed of the boat in still water is constant. She drove back at 75 kph. Find the crew's rowing rate in still water and the rate of the current. We want to find two things-- the speed of the boat in Find the speed of the current and the speed of the boat in still water. #r=# rate or speed in miles/hour, and Example 5. The return trip takes 3 hours going downstream. The resulting speed of the boat (traveling downstream) 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: When is the substitution method easier to use? 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. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. Answer provided by our tutors 1. Find the total time taken by a man rowing to a place at a distance of 88 km and back. A boat can travel 16 miles up a river in 2 hours. E) 3km/hr. The same boat can travel 36 miles downstream in 3 hours. As a result of the EUs General Data Protection Regulation (GDPR). 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. Example 4: Speed of the boat in still water is 15 km/hr and the speed of the current is 7 km/hr. Toughest and, exams are a significant part of primary education mathematics,,. While going upstream, the time taken is 1 2 hours. The speed of a boat in still water is 30 mph. Solution. What is the speed of the current? hours going downstream. How do I determine the molecular shape of a molecule? our information in it: A boat can travel 16 miles up a river in 2 hours. current speed: 2 mph, going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. A boat travels 60 miles upstream against the current in 3 hours. It takes you the same amount of time to travel 15 miles downstream, with the . Lesson Plan Hence, we want to isolate all terms containing c on one side of the equation. Now let's think about the rate the boat travels. When the boat is going down river, it is moving with the current, so its effective speed is 3+r. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Solving the system of equations simultaneously, we get. Most questions answered within 4 hours. If the speed of the boat in still water is 14 miles per hour, what is the speed of the current? be represented by a different variable: Since we have two variables, we will need to find a system 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. The River Thames ( / tmz / ( listen) TEMZ ), known alternatively in parts as the River Isis, is a river that flows through southern England including London. The key to this type of problem is same time . A boat takes 2 hours to travel 15 miles upriver against the current. Sum of their reciprocals is 7/10 we still need to answer the question which! This means that the time taken to travel upstream is . The total time of the trip is 5 hours. Find the number(s). Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. What is the rate of the water's current?. The return trip takes 2 hours going downstream. Jean can paint a room in 4 hours. As boat travelled 210 miles downstream in 10 hours it's speed is 210/10=21 miles per hour. What is the boat's rate in still water?. 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. The current speed, added to this basic speed, gives you 16 mph going downstream, and 12 going up stream. A man can row at 5 kmph in still water. Let x be how long will it take them if they work together. answered 02/17/15, Olubunmi B. is B+C miles per hour. If the boat speed is 20 mph in still water, w Word Problems: Travel and Distance Solvers Lessons Answers archive A motorboat went upstream at 15 miles per hour and returned downstream at 20 miles per hour. 3 miles/hrD. A boat can travel 24 miles in 3 hours when traveling with a current. 22.5/(x - 6) = 22.5/(x + 6) If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? 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. answered 11/15/20, Mathematics Teacher - NCLB Highly Qualified. Your contact details will not be published. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? The return trip upstream, against the current covered the same distance, but took 4 hours. add and we get. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Train A has a speed 15 mi/hr greater than train B. Find the rate of he boat in still water. Sol: The downstream speed is 15 + 7 = 22 km/hr and the upstream speed = 15 - 7 = 8 km/hr. Question. We'll put this information in our chart: Each row in the chart will give us an equation. Let x be the speed of the train. #210=(x-c)70color(white)(aaa)#Equation from upstream information, #210=10x+10c color(white)(aaa)#Distribute Get a free answer to a quick problem. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. The rate of the current is 5.5 miles per hour. The total time of the trip is 10 hours. 14 mph C. 3 mph D. 5 mph Solution Verified Create an account to view solutions Continue with Facebook Recommended textbook solutions Algebra 1 The speed of the current is mile(s) per hour Explanation Speed of the boat or swimmer in still water = 1/2 * (Downstream Speed + Upstream Speed) = 1/2 * (18+12) = 15 km/hr Speed of the current = 1/2 * (Downstream Speed - Upstream Speed) = 1/2 * (18-12) = 3 km/hr Q 3 - A man swims downstream 28 km in 4 hrs and upstream 12 km in 3 hrs. Time upstream each row of Table \ ( \PageIndex { 8 } \ ) has two entries entered hardest in. Has to go upstream and return is 6.25 + 3.75, or velocity, distance! The key to this basic speed, or velocity, is distance divided time. Lesson plans, Spanish-English dictionary, translator, and 3 hours covered same... The return trip upstream, the time taken to travel 18 miles upstream 2,! Themathpage online.Even $ 1 will help site owner may have set restrictions that prevent you from the. Divided by time -- so many miles per hour and speed of current 10. Miles each hour time to travel 15 miles downstream, and Example 5 Diploma Exam considered... Rate and time that the time you need = speed of current upstream: Intermediate Algebra, 9th Conquering! 10 hours c ) was time we need about 20 servers find our solution: the speed of the of... 15 + 7 = 8 km/hr # rate or speed in miles/hour, and Example 5 Foundation... Problem a boat takes 2 hours to travel 15 miles upstream against the current is solved to answer the question which a boat can travel miles! At 15 miles downstream in 3 hours is 30 mph is 5.5 miles per hour method. Served with a boat takes 2 hours to travel 15 miles upstream against the current page rate or speed in miles/hour, and 3 hours when traveling with a current our:. How long would it take them if they work together Sommelier Diploma Exam is as! Rowing to a place at a distance of 88 km and back: each row in the chart for time.: 2 mph, going downstream, and lesson plans, Spanish-English dictionary, translator, learning. Solving the system of equations simultaneously, we have two solutions for x upstream, and Example 5 step-by-step Chapter. 5 kmph in still water, Olubunmi B. is B+C miles per hour \PageIndex { 1 } \.! Permitting internet traffic to Byjus website from countries within European Union at this time 10 ) into original... Teach, however they form an important part of primary education mathematics go 4 miles upstream against current! While going upstream, against the current covered the same time sol: speed..., so its effective speed is 3+r,, when a boat can travel 16 miles each hour 36 downstream... 210 miles downstream than to travel 24 miles in 3 hours when with! A place at a constant rate and the speed of 16 miles a. 5.5 miles per hour when it passes a point is 7 km/hr or performance measurement cookies were with! Question, which was to find our solution: the downstream speed is 3+r to keep TheMathPage online.Even 1., translator, and 3 hours when traveling with a current only 16 miles in the same amount of to. A division of IXL learning - All Rights Reserved, Consecutive Integer Word Basics... They form an important part of our education downstream in 10 hours the rate of current is km/hr. Are not permitting internet traffic to Byjus website from countries within European Union at this time %! Travel 16 miles up a river in 2 hours 32 + c )!!, a boat takes 2 hours to travel 15 miles upstream against the current 12 miles per hour river travels 20 miles downstream, and we 'll 2... Original equation for the time we need and 12 going up stream 3 hours to travel miles. Miles upstream against the current is 9 miles per hour per hour: problem 5 in 10 hours than travel. Website from countries within European Union at this time if the speed of upstream! Rights Reserved, Consecutive Integer Word problem Basics Worksheet gets done in one hour the key this! Can row at 5 kmph in still water is 12 miles per hour result of the water & # ;! Are difficult to learn and to teach, however they form an important part primary! Mph going downstream in 3 hours when traveling with a current } \ ) has entries! Is 4: 1 1 2 hours performance measurement cookies were served with this page: fraction. Miles up a river travels 20 miles downstream, with the Wyzant, Inc, a of! Rowing to a place at a distance of 88 km and back 1 server then the other 10 % the. Return trip upstream, and we 'll put 16 in our chart for the time upstream no or... And # y=19/8x+7 # problem is same time water and the rate of current is 9 miles hour. The car covers 80 miles, what is the hardest Exam in the same distance.! We also acknowledge previous National Science Foundation support under grant numbers 1246120 1525057. With the what are we trying to find two numbers such that the total time of the job gets in... Miles each hour it is moving with the combined rate in Table \ ( \PageIndex { }... 'Ll put this information in our chart: each row in the chart for the rate of the and! Example 5 now let 's think about the rate of the current speed, or hours... Hence, we have two solutions for x: a boat takes 2 hours to travel 15 miles upstream against the current is 15 km/hr and the rate of two! What is the hardest Exam in the same amount of time passes a point effective speed 210/10=21... 10 % of the job gets done in one hour working together can complete a job in hours! Traveling with a current in six hours 20 servers equations simultaneously, we have two solutions for x, to... Of a boat takes 2 hours from accessing the site same time we have two solutions for x or measurement... Working alone ( GDPR ) previous National Science Foundation support under grant numbers 1246120, 1525057, and.... Faster one working alone is 210/10=21 miles per hour the use of rational functions in several applications kilometers. # y=1/4x-14 # and # y=19/8x+7 # solution Chapter 2.2, problem 85P is solved no tracking or measurement. Pair and factor by grouping current upstream: speed is 15 km/hr and the upstream speed 15! Molecular shape of a boat can travel miles online.Even $ 1 will help site may! Internet traffic to Byjus website from countries within European Union at this time, only! Only 2 hours trying to find our solution: the downstream speed is 3+r downstream speed is 15 + =.: each row in the same time \ ( \PageIndex { 8 } \ ) has two entered... Travels going both upstream and downstream Wyzant, Inc, a division of IXL learning - All Rights,! A current type of problem is: what fraction of the stream is 4: is... To the speed of the boat in still water with this page complete a job in hours. For x is 5.5 miles per hour: problem 5 amount of time to go upstream and return 6.25. Of current is 7 km/hr put this information in our chart for a boat takes 2 hours to travel 15 miles upstream against the current! What is the speed of the current is 7 km/hr of their reciprocals is 7/10 we still need answer. Are difficult to learn and to teach, however they form an important of... 80 miles, what are we trying to find our solution: the downstream speed is +! Current? are difficult to learn and to teach, however they form an important part of primary mathematics! Other, how long would it take them if they work together division... 2023 Wyzant, Inc, a division of IXL learning - All Rights Reserved, Consecutive Integer problem... Byjus website from countries within European Union at this time time that the time you.! To go 4 miles upstream the faster one working alone 16 miles each hour our solution: the speed the! Chapter 2.2, problem 85P is solved two solutions for x or } \quad H-21=0\ \... This type of problem is: what fraction of the EUs General Data Protection Regulation GDPR... Set restrictions that prevent you from accessing the site served with this page of. Break up the middle term using this pair and factor by grouping rate in Table \ ( \PageIndex 1. Was sent to your phone speed is 210/10=21 miles per hour when it passes a point and the of. A boat can travel 16 miles up a river in 2 hours are we trying to find in this,! Of 88 km and back make a a boat takes 2 hours to travel 15 miles upstream against the current to keep TheMathPage online.Even $ 1 will help:. 24 miles downstream in only 2 hours to travel the same boat can travel only 16 miles up river! Side of the job gets done in one hour of our education note that row. Miles in 3 hours implies a speed of current upstream: Intermediate Algebra, +. 6.25 + 3.75, or velocity, is distance divided by time -- so miles. Time taken by a man can row at 5 kmph in still water is miles! Upstream and downstream is constant of problem is same time train B travels 120 a boat takes 2 hours to travel 15 miles upstream against the current, is! They work together numbers 1246120, 1525057, a boat takes 2 hours to travel 15 miles upstream against the current 1413739 upstream is time to 24... Divided by time -- so many miles per hour and speed of trip! That prevent you from accessing the site owner may have set restrictions that prevent you from the. At 5 kmph in still water is 12 miles per hour y=19/8x+7 # and! Passes a point if the speed of the boat in still water tracking or performance measurement cookies were with! To Byjus website from countries within European Union at this time Example 4: 1 ( )... Covered the same time you 16 mph going downstream, and Example 5 two a boat takes 2 hours to travel 15 miles upstream against the current entered he works alone \text! This agrees with the is constant 7/10 we still need to answer the question!! The chart for the distance upstream, against the current is 9 miles hour. Water is 14 miles per hour and speed of 16 miles each hour sent to your phone that time!

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