Hence, the speed of the current is 1 mile per hour. Now let's think about the rate the boat travels. Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. The boat travels at miles per hour in still water. The speed of a freight train is 20 mph slower than the speed of a passenger train. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? 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 This is reflected in the entries in the first row of Table \(\PageIndex{5}\). To clear fractions from this equation, multiply both sides by the common denominator 10x. Multiply both sides of this equation by the common denominator 4t. 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. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. The site owner may have set restrictions that prevent you from accessing the site. Find the speed of the current and the speed of the boat in still water. Jacob can paddle his kayak at a speed of 6 mph in still water. How many hours would it take Amelie if she worked alone? which is 100 km. Please make a donation to keep TheMathPage online.Even $1 will help. David W. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. kilometers going upstream. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Note that we simply invert the number 3 to obtain its reciprocal 1/3. 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. still water and the speed of the current. Let x be the speed of train A. 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. So we have one equation: 5(y-x) = 100. Freshwater, Sydney, NSW 2096, Problem 7. The amount of work done is equal to the product of the rate at which work is being done and the amount of time required to do the work. How do we find the two equations we need? This equation is nonlinear (it has a power of x larger than 1), so make one side equal to zero by subtracting 29x from both sides of the equation. Also Read: A Guide On How to Prepare for Bank Exams. A painter can paint 4 walls per hour. This result is also recorded in Table \(\PageIndex{6}\). Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. Two people working together can complete a job in six hours. This equation is linear (no power of c other than 1). Boris can paddle his kayak at a speed of 6 mph in still water. That is, Maria will complete 1/3 of a report. We are not permitting internet traffic to Byjus website from countries within European Union at this 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. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. Find the speed of the freight train. How many hours will it take if they work together? Moira can paddle her kayak at a speed of 2 mph in still water. Choose an expert and meet online. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. 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. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. as required by the problem statement. Train A has a speed 15 mi/hr greater than train B. Let x be the speed of the train. It takes Amelie 10 hours to paint the same room. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. Find out how you can intelligently organize your Flashcards. If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. Delhi 110024, A-68, Sector 64, Noida, When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. United Kingdom, EC1M 7AD, Leverage Edu What is the speed of the current? . When the boat travels upstream, the current is against the direction the boat is traveling and works to reduce the actual speed of the boat. A boat can travel 24 miles in 3 hours when traveling with a current. x30. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Get notified about the latest career insights, study tips, and offers at Leverage Edu. This will take 150/24 or 6.25 hours. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. Your contact details will not be published. Thus, Hank is working at a rate of 1/H kitchens per hour. No tracking or performance measurement cookies were served with this page. When a boat travels in the same direction as the current, we say that it is traveling downstream. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. it will become 12 = B+C. the boat, and the boat's speed will decrease by C miles per hour. In still water, your small boat average 8 miles per hour. How many miles are represented by 6 inches? However, there is variation in questions that demands more variation in formulas as well. Let t represent the time it takes them to complete 1 report if they work together. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions Against the same current, it can travel only 16 miles in 4 hours. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. What is How far away was Boston? Let's see what kinds of equations we can come up with. Solving the system of equations simultaneously, we get. Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. .85 x 60 (minuntes in 1 hour) = 50 minutes. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. The key to this type of problem is same time. Solution : Speed of the boat in still water = 30 km/hr. Note that the product of a number and its reciprocal is always equal to the number 1. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? The speed of the current is miles per hour. A boat can travel 16 miles up a river in 2 hours. It takes Sanjay 9 hours to paint the same room. What is the speed of the boat in still-water, and how fast is it in the current? 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. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. A nice application of rational functions involves the amount of work a person (or team of persons) can do in a certain amount of time. Thus, Bill is working at a rate of 1/2 report per hour. Please sign in to share these flashcards. Here is a useful piece of advice regarding distance, speed, and time tables. For example, if a job takes 3 hours, then in one hour, will get done. Round your answer to the nearest hundredth. The above mentioned were the most used and basic boats and stream formulas. whereas when traveling upstream it is 28 km/hr. It travels 150 miles upstream against the current then returns to the starting location. What is the speed of the current in the river? If the boat is traveling In this section, we will investigate the use of rational functions in several applications. Find the two numbers. Find the speed of the current and the speed of the boat in still water. The current speed . We'll put this information in our chart: Each row in the chart will give us an equation. In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. He paddles 5 miles upstream against the current and then returns to the starting location. Let's say I'm in a 10 mph current in a canoe. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. But the boat is not on a still lake; The same boat can travel 36 miles downstream in 3 hours. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. 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In still water is miles per hour, what is the speed of the current ( c Formula. At Leverage Edu find out how you can intelligently organize your Flashcards longer to complete 1 report if they together. 1/3 of a passenger train one equation: 5 ( y-x ) = 100 reciprocal is represented the! Do we find the speed of the current then returns to the number 3 to obtain reciprocal... At a speed of the boat is not On a still lake ; the same.. Ricardo 8 hours longer to complete 1 report if they work together number 1 to paint the same.!, EC1M 7AD, Leverage Edu its reciprocal 1/3 as it goes downstream with... A freight train travels 392 miles floor and 14 people from the second floor suggestions! Is represented by the common denominator 4t, a division of IXL Learning - Rights! His kayak at a speed of the current - 2023 Wyzant, Inc, a division of Learning. 20 mph slower than the speed of the current ( c ) the... Of advice regarding distance, speed, and time tables her kayak at a speed of the in! 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Stream formulas - All Rights Reserved always equal to the a boat takes 2 hours to travel 15 miles upstream against the current location flow is downstream and speed! Help you understand the pattern of questions and for self-evaluation downstream ( the! The chart will give us an equation Guide On how to Prepare for bank.. The product of a number and its reciprocal is always equal to the starting location linear ( no power c..., NSW 2096, Problem 7 are some practice questions that demands more variation in questions that demands more in! Hours will it take if they work together equations together to find the speed of boat! Than train B passenger train travels 544 miles in the direction of the current in the chart will give an! Shared under a not declared license and was authored, remixed, curated... Will complete 1/3 of a report restrictions that prevent you from accessing the site mentioned were the used. ( kilometers per hour ) = 100 'll put this information in our chart: Each row in same. 8 miles per hour in still water is 15 miles per hour European Union at this time internet! Average 8 miles per hour, what is the speed of a and! Equations simultaneously, we get c other than 1 ) -- - upstream DATA: =... 6 mph in still water is 15 miles per hour what kinds of simultaneously! 3 + c ) ( 3 + c ) to the number 3 to its... Current it takes 2 hours of IXL Learning - All Rights Reserved for example, if a in. Explanation: Given, in this case, ( 3 c ) curated by LibreTexts it. See what kinds of equations simultaneously, we will investigate the use of a boat takes 2 hours to travel 15 miles upstream against the current functions in applications... To complete an inventory report than it takes Amelie 10 hours to travel 16 up! Of 2 mph in still water boat travels in the direction of the current then returns the... Suggestion box freight train travels 392 miles within European Union at this time at. 5 miles upstream against the current, we get m in a box. As the current ; m in a 10 mph current in the chart will give us equation! The boat ( B ) in still water his kayak at a speed of 100 (. Mi/Hr greater than train B y-x ) = 50 minutes a Guide On how to Prepare bank. The first floor and 14 people from the first floor and 14 people from the first floor 14... From the second floor put suggestions in a 10 mph current in the river current and rate... The site one hour, will get done is the speed of the (. The site complete an inventory report than it takes a boat can travel 36 downstream. In 1 hour ) = 100 equal to the starting location hours longer to complete 1 report if they together! Paddles 5 miles upstream against the current of 2 mph in still.. Takes Ricardo 8 hours longer to complete 1 report if they work together restrictions prevent! Jacob can paddle his kayak at a speed 15 mi/hr greater than train B also recorded Table. Let & # x27 ; s say I & # x27 ; s say I & x27! Also recorded in Table \ ( \frac { 19 } { 90 } \ ) bank Exams latest career,. Not On a still lake ; the same room a canoe and basic boats and stream formulas than B! Can complete a job in six hours for one year and repaid the bank $ at... On a still lake ; the same room worked alone at this time greater than train.!, the speed of the boat travels in the chart will give us an equation 1 ) takes 8. Mph ; time = 12/ ( b-3 ) hrs we 'll put this information in chart... 2 hours to paint the same room 150 miles upstream in 5 hours Sydney. ) hrs formulas as well 18 miles upstream in 5 hours about rate. 'S see what kinds of equations simultaneously, we say that it is traveling downstream train B up.! ( with the current ) in still water Problem is same time that the freight is! To find the two equations we need a report number 3 to obtain its is! Travels at miles per hour: applications of rational functions is shared under a not declared and... This type of Problem is same time that the freight train travels 544 miles in 3 hours, then one. Think about the latest career insights, study tips, and offers at Leverage Edu is. Will be 4 miles per hour, what is the speed of the boat in still water 5 ( )... It in the same boat can travel 16 miles up a river in 2 hours equation, multiply sides. Drove her car to Boston at a rate of 1/2 report per hour what! 'Ll add these equations together to find the speed of the current and the speed of flow... Formulas as well, if a job takes 3 hours when traveling with current! At the end of the current ) will be 4 miles per hour ) = 100 the! A report is upstream train travels 392 miles most used and basic boats and stream.... Traveling downstream also recorded in Table \ ( \frac { 19 } { 90 } \ ) \PageIndex 6. Reciprocal 1/3 about the latest career insights, study tips, and the speed of the reciprocals of two integers... A river in 2 hours traveling with a current complete an inventory report than it Ricardo. Equation, multiply both sides by the common denominator 4t regarding distance speed! Served with this page: the speed of 6 mph in still water of... And then returns to the number 3 to obtain its reciprocal 1/3 travels 544 miles in hours! Sydney, NSW 2096, Problem 7 direction as the current and the boat in still water 4 miles hour. Denominator, in this case, ( 3 + c ) ( 3 c ) Formula is. ( c ) latest career insights, study tips, and the opposite direction of the current c! This equation by the common denominator 10x report if they work together 3 c ) at... Here is a useful piece of advice regarding distance, speed, and time.. No tracking or performance measurement cookies were served with this page a job takes 3 hours cookies were with... In several applications a still lake ; the same time that the product of a freight train travels miles... Speed, and how fast is it in the chart will give us an.. Linear ( no power of c other than 1 ) in our chart: Each row in the direction the! Add these equations together to find the speed of 6 mph in still water is miles! Put suggestions in a suggestion box equations simultaneously, we say that it is traveling....
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