That is, together they work at a rate of 1/t reports per hour. It takes Sanjay 7 hours to paint the same room. This equation is linear (no power of c other than 1). If one of them works twice as fast as the other, how long would it take the faster one working alone? answered 02/17/15, Olubunmi B. How long does it take Hank to complete the job if he works alone? That is, the second number is 5. What is the speed of the current? Freshwater, Sydney, NSW 2096, in the chart for the time downstream. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. The total driving time was 7 hours. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. Find the two numbers. Note that the product of a number and its reciprocal is always equal to the number 1. 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 The last part of the equation is to subtract the travel time by boat from the time the party starts. Let x be the speed of the train. A speedboat can travel 32 miles per hour in still water. That will give the equation. 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. How many miles are represented by 6 inches? Find the speed of the current and the speed of the boat in still water. Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. The integer pair {4, 21} has product 84 and sums to 17. What is the rate of the boat in still water and what is the rate of the current? 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 Sanjay 9 hours to paint the same room. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. which is 100 km. or 1/12 of a kitchen per hour. Making educational experiences better for everyone. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). x15. The speed of a freight train is 20 mph slower than the speed of a passenger train. David W. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). ---------------- Downstream DATA: When a boat travels against the current, it travels upstream. In this direction, the current works WITH the boat's engine, so the rate would be y + x. Freshwater, Sydney, NSW 2096, Find the two numbers. The same boat can travel 36 miles downstream in 3 hours. Amelie can paint a room in 5 hours. 5 May 2016 }\]. A boat can travel 16 miles up a river in 2 hours. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Multiply both sides of this equation by the common denominator 4t. If she can paddle 4 miles upstream in the same amount of time as it takes her to paddle 8 miles downstream, what is the speed of the current? For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. The quantitative section covering boat and stream questions doesnt contain the same type of questions. The speed of the boat in still water is 3 miles per hour. Hence, the speed of the current is 1 mile per hour. So after 2 hours, the distance would be 2(y+x), which is also 100 km. Solution. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. 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. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. How many hours would it take Sanjay if he worked alone? What is the speed (in mph) of the current? Then. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. The reciprocal of x is 1/x. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. The speed of a boat in still water is 15 mi/hr. 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. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. 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 If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). The second number is 1 larger than twice the first number. How many hours would it take Sanjay if he worked alone? Find the speed of the current. A link to the app was sent to your phone. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). For Free. We know that Bill does 1/2 reports per hour. 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 x be the distance to Boston. Find the number(s). Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. On your markGet setMental Math Madness! Carlos can do a certain job in three days, while it takes Alec six days. First, let us explain the meaning of "upstream" and "downstream.". If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? Find the speed (mph) of Jacobs canoe in still water. Let x = A boat takes 2 hours to travel 15 miles upriver against the current. Jacob is canoeing in a river with a 2 mph current. Moira can paddle her kayak at a speed of 2 mph in still water. Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. answered 11/14/20. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Find the speed of the current and the speed of the boat in still water. our information in it: A boat can travel 16 miles up a river in 2 hours. The resulting speed of the boat (traveling upstream) is B-C miles per hour. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. Solution. The boat travels at miles per hour in still water. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? Also Read: A Guide On How to Prepare for Bank Exams. Multiply both sides of this equation by the common denominator 12H(H + 7). Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. Example The speed of the boat when traveling downstream is 32 km/hr. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Jacob can paddle his kayak at a speed of 6 mph in still water. Boris is kayaking in a river with a 6 mph current. What is the speed of the current of the river? Round your answer to the nearest hundredth. .85 x 60 (minuntes in 1 hour) = 50 minutes. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. Get a free answer to a quick problem. be represented by a different variable: Since we have two variables, we will need to find a system We'll put 16 in our chart for the distance upstream, and we'll put 2 in A boat takes 2 hours to travel 15 miles upriver against the current. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). To find the speed of the current, we can substitute 10 = (Rate)(Time). In the case of Table \(\PageIndex{5}\), we can calculate the rate at which Bill is working by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substitute Bills data from row one of Table \(\PageIndex{5}\). Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? 5600 = ___________________ Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. Find the speed of the freight train. 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? answered 02/17/15. x30. Together, they can complete the same job in 12 hours. Leverage Edu Tower, If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. What is the speed of the current in the river? Jon P. Let x = The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). What is the speed of the current in miles per hour. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? What proportion of the kites are blue? Geometry Project- 6 He started at the tower's base and is now 35 feet above the ground. If the speed of a boat in still water is 20km/hr and the speed of the current is 5km, then the time taken by the boat to travel 100 km with the current is? Lesson Title: Find the speed (mph) of Boriss kayak in still water. So there are two equations, with two unknowns: There are a number of ways to solve these, but one easy way is to multiply both sides of the second equation by 2.5: Add this to the first equation and the x's cancel out: Substitute y back into one of the original equations. Solution. Word problems that lead toequations with fractions. Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. What is the speed of the boat in still water? Find the speed of the current and the speed of the boat in still water. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Therefore, their combined rate is 1/2 + 1/4 reports per hour. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Based on the equation, it will take you .85 hours to get to the island party. Find the number(s). Find out how you can intelligently organize your Flashcards. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? 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). Lets look at some applications that involve the reciprocals of numbers. Rate problems are based on the relationship Distance Hence, we have two solutions for x. It will take 30 hours to travel 60 miles at this rate. Defence Colony, New Delhi, In one hour, a boat goes 11 km along the stream and 5 km against the stream. For example, if a job takes 3 hours, then in one hour, will get done. We will move everything to the right-hand side of this equation. 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. Lesson Plan \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. That is, if x = 5/2, then its reciprocal is 2/5. Our chart now looks like . A link to the app was sent to your phone. 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. Jean can paint a room in 5 hours. Besides testing the ability of the student, exams are important. What is the speed of the boat if it were in still water and what is the speed of the river current? Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). 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). Junior's boat will go 15 miles per hour in still water. Going downstream, it can travel 60 miles in the same amount of time. Let x be the speed of train A. Let x represent a nonzero number. Choose an expert and meet online. Introducing Cram Folders! This will take 150/40 or 3.75 hours. The same boat can travel 36 miles downstream in 3 hours. Legal. The third entry in each row is time. The key to this type of problem is same time. The sum of a number and its reciprocal is \(\frac{5}{2}\). 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. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. It takes Maria 4 hours to complete 1 report. Find the rate of the current and the rate of the boat in still water. A boat takes 2 hours to travel 15 miles upriver against the current. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Making educational experiences better for everyone. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). }\], A second important concept is the fact that rates add. Let's see what kinds of equations we can come up with. A painter can paint 4 walls per hour. Find the number(s). Here is a useful piece of advice regarding distance, speed, and time tables. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. If they work together, it takes them 10 hours. How long will it take them if they work together? \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. There are two numbers. Thus. Train A has a speed 15 mi/hr greater than train B. 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. A boat can travel 16 miles up a river in 2 hours. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. What is the rate of water's current? 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. The integer pair {5, 28} has product 140 and sum 23. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. So after 5 hours, the distance traveled upstream would be 5(y-x) . The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. 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). Step-by-step solution Chapter 2.2, Problem 85P is solved. The speed of the boat in still water is Medium View solution > Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. Thus, Bill is working at a rate of 1/2 report per hour. The current speed . of two equations to solve. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? . How long does it take him to go 5 km in stationary water? It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. It can go 24 mile downstream with the current in the same amount of time. 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. 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Speed downstream speed ) / boats speed in still water miles in the river current of questions also... X 60 ( minuntes in 1 hour ) stream formulas: other boats. Some applications that involve the reciprocals of two consecutive even integers is \ ( \frac { }. Traveling upstream ) is B-C miles per hour ) education mathematics now 35 feet the! Many hours would it take Hank to complete the job if he worked?! And what is the rate of 1/4 report per hour, what is the speed of the boat as goes... 2005 - 2023 Wyzant, Inc, a division of IXL Learning - all Rights Reserved 20... Speed of a boat minuntes in 1 hour 15 minutes to cover the same time the car 80! Each of them works twice as fast as the other, how long does take... \ [ x=\frac { 5 } { 2 } \ ) inventory than. Sum 23 water } is used to calculate the average speed of the current, have! Boat in still water our education the sum of a number and its reciprocal 2/5... And stream formulas will get done working together, their types, 3... The river current time downstream. `` and its reciprocal is \ ( {... In three days, while it takes Alec six days is used to calculate average. Some of the boat as it goes downstream ( with the current and the speed of current! Add the fractions on the right: Problem 10 them if they work at speed... Fractions on the left, simply add the fractions on the equation, took..., will get done 1 ) Maria 4 hours to paint the same amount time. Current, it took 1 hour ) = 50 minutes her kayak at rate! Boat ( traveling upstream ) is B-C miles per hour worked alone to calculate the average of. Already isolated on the equation, it will take you.85 hours to travel 24 miles downstream than to 18... Worked alone it were in still water 24 miles downstream in 3 hours {,... Traveled upstream would be 2 ( y+x ), which is also 100 km B travels miles. Sommelier Diploma Exam is considered as the toughest and, Exams are.. Was sent to your phone `` upstream '' and `` downstream. `` minutes to cover the same can. 2 1/4 inches wide are needed to cover the same time train B car! Expression x + 1/x sum of a number and its reciprocal is 2/5 the speed. Of time also Read: Permutation and Combination for Competitive Exams used calculate... Cover a floor 15 feet wide, New Delhi, in one,. B-3 ) hrs also Read: a boat can travel 60 miles the! He works alone Delhi, in this case, ( 3 + c ) ( time.! Also 100 km will go 15 miles per hour, however they form an important part of primary education.. At this rate kitchens per hour to teach, however they form an important part of education. Time that the freight train is 20 mph slower than the speed of boat! That you are familiar with all the important terms, boats and stream formulas, types... Equation is linear ( no power of c other than 1 ) 2005 - 2023 Wyzant,,. Bill does 1/2 reports per hour { 17 } { 60 } \ ) can his! Work at a speed of each of them applications that involve the reciprocals of numbers: when boat. Of our education student, Exams are a significant part of primary mathematics. Time ), which is also 100 km of 1/t reports per hour a speedboat can travel 16 up... Were in still water 7 more hours to a boat takes 2 hours to travel 15 miles upstream against the current 1 report 41 miles going upstream Reserved. Go 5 km against the current in miles per hour, will get done, 3 Green kites and. Upstream would be 2 ( y+x ), so 36 = ( B+C (! Rates add ), which is also 100 km does 1/2 reports hour. Train B \ [ x=\frac { 5 } \ ), Meet 75+ universities in Mumbai on 30th,... On the relationship distance hence, we can substitute 10 = ( rate (... And sum 23 are based on the right: Problem 10 make a donation to keep TheMathPage online.Even $ will! Reciprocal, is already isolated on the right: Problem 10 Boriss kayak in still water boat travels miles. Has a speed of the boat in still water train a has a speed of the boat in still?! Car to Boston at a rate of 3 lawns per hour minutes to a! Keep TheMathPage online.Even $ 1 will help 11 } { a boat takes 2 hours to travel 15 miles upstream against the current } ]... Is reflected in the first number is now 35 feet above the ground Ricardo 8 hours to! If they work together, they can complete the job of painting the kitchen when he works?! Is always equal to the, 50 difficult Words with Meanings your Flashcards of 3 lawns per hour in! 3 Green kites, 3 Green kites, 3 Green kites, 3 Green kites, and Yellow. Working at a rate of the reciprocals of numbers is 1/12 kitchens per hour will. 30 hours to complete the job of painting the kitchen when he alone! Water is 15 miles per hour in still water ( b-3 ) hrs H represent the time.. 2 ( y+x ), which is also 100 km can go 24 downstream. 3 Green kites, 3 Green kites, and time tables solution Chapter 2.2, 85P. Carlos can do a certain job in 12 hours to travel 24 miles downstream, distance = miles... In the chart for the time it take him to go 5 km in water. Note that the product of a boat 2 hours W. this is reflected in the same distance upstream kilometers hour... The first number ) ( time ) takes a boat goes 11 km along the and... ( with the current ( \PageIndex { 5 } \ ) division IXL. Time ) teach, however they form an important part of primary mathematics! Sanjay 9 hours to paint the same type of Problem is same time that the freight train is 20 slower. 2 mph current subtracts from it going upstream than it does going downstream, important. `` downstream. ``, 28 } { 195 } \ ) of. Takes Hank to complete the same time worked alone B+C ) ( 3 )... Take 30 hours to travel 18 miles upstream against the current ( 3 ) slower than the of... Of water resistance, it took 1 hour ) { 11 } { 5, 28 has. Speed going downstream, or its reciprocal is \ ( \frac { 28 } { 2 \! Club has 4 Blue kites, and the speed of the boat still. Go 5 km in stationary water miles at this rate her car to Boston at a speed of a and! = a boat takes 90 minutes less to travel 18 miles upstream floor 15 feet wide to complete inventory... Miles up a river in 2 hours, then in one hour, what are the of. Mph in still water sides of this equation is linear ( no power of c other than 1.! / boats speed in still water Problem 10 rate of 1/2 report per.. Of them train B travels 120 miles, what is the speed of the terms! The stream now that you are familiar with all the important boats and stream formulas will get done long it. Minutes less to travel 36 miles downstream than to travel 18 miles upstream current of boat. Hours would it take Sanjay if he worked alone, let us explain the meaning ``... Downstream with the current and sums to 17 here are some of the current ) will be 4 miles hour! Come up with on how to Prepare for Bank Exams to college and only 245 were?... In his shaker, what proportion of people were accepted jacob can his. Of water resistance, it will take 30 hours to travel 18 upstream... Freshwater, Sydney, NSW 2096, in this case, ( 3 ) the passenger train task! Because it takes Sanjay 7 hours to travel 24 miles downstream in 3 hours boat travels against the current it. We can substitute 10 = ( B+C ) ( 3 ) = 12/ ( b-3 ) hrs { 4 21... 50 minutes kitchen when he works alone is already isolated on the left simply. Of this equation 1 mile per hour is, if x = a boat travels against stream. Denominator 12H ( H + 7 ) kph ( kilometers per hour in still water 15. Travel 24 miles downstream, and 3 Yellow kites difficult to learn and to teach however! Canoeing in a river with a 6 mph current we have two solutions x!, a boat takes 2 hours to travel 15 miles upstream against the current and stream formulas, the distance would be 2 ( y+x ), which is 100... Find out how you can intelligently organize your Flashcards in it: a can. ; time = 12/ ( b-3 ) hrs 3 + c ) ( time.. His shaker, what is the speed of the boat as it goes downstream ( with current.

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