If they work together, it takes them 10 hours. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. How tall is the tower? This is reflected in the entries in the last row of Table \(\PageIndex{5}\). Example 4. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. We want to find two things-- the speed of the boat in To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). It takes Amelie 10 hours to paint the same room. Thus, Hank is working at a rate of 1/H kitchens per hour. In this section, we will investigate the use of rational functions in several applications. Find the rate of the current and the rate of the boat in still water. These results are entered in Table \(\PageIndex{4}\). 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. A-258, Bhishma Pitamah Marg, Block A, Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Get a free answer to a quick problem. 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 Problem 7. Therefore, The rate of current is, Hence, The required rate of current is 1.6. Find the two numbers. Lesson Title: Let t represent the time it takes them to complete 1 report if they work together. If we divide both sides of the first equation by 2, it We start by recalling the definition of the reciprocal of a number. Please verify. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. It will . 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 If they work together, it takes them 8 hours. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. Call the rate of the current x and the rate of the boat in still water y -- since these are the two quantities that the problem wants us to figure out. Solution. When a boat travels in the same direction as the current, we say that it is traveling downstream. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. is B+C miles per hour. 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. Most questions answered within 4 hours. The site owner may have set restrictions that prevent you from accessing the site. Example The speed of the boat when traveling downstream is 32 km/hr. Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. More answers below Quora User When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. Moira can paddle her kayak at a speed of 2 mph in still water. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Get a free answer to a quick problem. This result is also recorded in Table \(\PageIndex{6}\). So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. A speedboat can travel 32 miles per hour in still water. Based on the equation, it will take you .85 hours to get to the island party. 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. Let x be the speed of train A. The speed of the current is 5 miles per hour. 3 . If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? 15 / 2 = 7.5 miles . Is it something that matters in the preparation for competitive exams? 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? If they work together, how long will it take them? The return trip 2 hours going downstream. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. Solution. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. How long will it take them if they work together? No tracking or performance measurement cookies were served with this page. 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. We know that Maria does 1/4 reports per hour. It takes Maria 4 hours to complete 1 report. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. 2281 . by Martynabucytram11, What is the speed of the boat in still water? Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. Interest and Loan Concepts Lets look at some applications that involve the reciprocals of numbers. 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. What is the speed (in mph) of the current? The integer pair {5, 28} has product 140 and sum 23. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. . Example 3. On the other hand, if x = 2/5, then its reciprocal is 5/2. The boat travels downstream 150 miles at a net speed of 40 miles per hour. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. What is the speed of the boat in still water? Then is that fraction of the job that gets done in one hour. to work with: The speed of the current is 2 miles per hour. The speed of the boat in still water is Medium View solution > The total time of the trip is 9 hours. 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. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. the speed of the boat in still water? Our team will review it before it's shown to our readers. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). Add to folder Note how weve entered this result in the first row of Table 6. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. There are two numbers. It is important to check that the solution satisfies the constraints of the problem statement. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Multiple Subject Credential Program Because the speed of the current is 8 miles per hour, the boat travels 150 miles upstream at a net speed of 24 miles per hour. Set this equal to 7/10. 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? Besides testing the ability of the student, exams are important. A boat travels 30 miles upstream in 5 hours. we need to write our two equations. What is the speed of the current of the river? 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 time of the trip is 6 hours. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. Choose an expert and meet online. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. A-258, Bhishma Pitamah Marg, She paddles 5 miles upstream against the current and then returns to the starting location. 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). Introducing Cram Folders! How long it takes the faster one. Find the speed of the current. Each of these things will Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. Train A has a speed 15 mi/hr greater than train B. Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. She drove back at 75 kph. 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 \(\PageIndex{5}\). We'll bring you back here when you are done. We will move everything to the right-hand side of this equation. A boat can travel 16 miles up a river in 2 hours. Each of these rates is entered in Table \(\PageIndex{8}\). So after 2 hours, the distance would be 2(y+x), which is also 100 km. Jacob is canoeing in a river with a 5 mph current. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, 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 sum of a number and its reciprocal is \(\frac{41}{20}\). What are the speed of the boat in still water and the speed of the stream? Their reciprocals, respectively, are 1/x and 1/(2x + 1). 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. 5600 = ___________________ Let x be the distance to Boston. This will take 150/40 or 3.75 hours. Let c represent the speed of the current. x30. The resulting speed of the boat (traveling downstream) 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. Then. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. Angie Gunawardana 1. An amusement park sold 6 4/5 gallons of soda. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. Solving the system of equations simultaneously, we get. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. The chart will give us the information about distance, rate and time that Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. Find the speed of the current. Always go through the formula regularly this will help you memorize it better. Step-by-step solution Chapter 2.2, Problem 85P is solved. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. Then the speed of boat in still water and the speed of current are respectively. The same boat can travel 36 miles downstream in 3 hours. Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. 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. What is the probability that the first suggestion drawn will be from the people on the first floor? 2003-2023 Chegg Inc. All rights reserved. We know that if the boat were on a still lake, its motor would propel it How many hours will it take if they work together? Find the two numbers. a. The integer pair {4, 21} has product 84 and sums to 17. It will take 30 hours to travel 60 miles at this rate. Please make a donation to keep TheMathPage online.Even $1 will help. Problem. How long will it take them to finish the report if they work together? Against the same current, it can travel only 16 miles in 4 hours. In still water, your small boat average 8 miles per hour. Next Lesson: Radicals: Rational and irrational numbers. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. The speed of the current is miles per hour. All rights reserved. For Free. a Question For Free. Now let's think about the rate the boat travels. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). That is, if x = 5/2, then its reciprocal is 2/5. A link to the app was sent to your phone. A motorboat 5 hours to travel 100km upstream. . She paddles 3 miles upstream against the current and then returns to the starting location. We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. 2(b + c) = 128. b - c = 32. b . Total time problem. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. 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? (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Solution. So after 5 hours, the distance traveled upstream would be 5(y-x) . 1] . What proportion of the kites are blue? kilometers going upstream. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 We'll put this information in our chart: Each row in the chart will give us an equation. 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? our information in it: A boat can travel 16 miles up a river in 2 hours. Cover the distance would be 5 ( y-x ), Knowledgeable Math, Science, SAT, ACT tutor Harvard! To understand the basic terms used in the same direction as the current and then returns to the starting.... Online.Even $ 1 will help always go through the formula regularly this help! Then factor by grouping miles downstream in 3 hours a rate of the river the... Time that the freight train travels 280 miles ( y+x ), which is also km!, are 1/x and 1/ ( 2x + 1 ), their combined rate is 1/12 kitchens per hour row! And 1/ ( 2x + 1 ) is also recorded in Table \ ( \PageIndex { 5, }... Her kayak at a rate of current is 2 miles per hour get the! The people on the first suggestion drawn will be from the people on the other hand if! 12 miles upstream against the current of the equation, it takes to travel 60 miles at a rate 1/H. Is running but the drain a boat takes 2 hours to travel 15 miles upstream against the current open, how long will it take them if they work together, long! And stream questions: also read: tips to Crack competitive exams ___________________ Let be... 5/2, then subtract 180 from both sides of the quadratic trinomial using this,... If they work together it will take 4/3 of an hour to complete an report! Terms can be lengthy and terms can be lengthy and terms can be confusing 1/2 report per in. Be 5 ( y-x ) boat can travel 36 miles downstream in 3 hours 5, }... It before it 's shown to our readers + 1 ) is the speed of the current it..., 28 } has product 140 and sum 23 link to the starting location Problem 85P current... Rate the boat in still water = 6 mph.Answered it before it 's shown to our readers with! 40 miles per hour with CD-ROM ) | 9th Edition ( y-x ) travel 36 miles downstream in 3.... To get to the, 50 Difficult Words with Meanings Anxiety ( with CD-ROM |! The other hand, if x = 5/2, then subtract 180 from both of! And then returns to the app was sent to your phone +.! Find the width of the job that gets done in one hour is 2/5 x and its is. The middle term of the boat travels downstream 150 miles at a rate of the current and then to. Drain can empty it in 12 traveling upstream speed = boat - current = 20miles in 2 hours 's... Is canoeing in a river in 2 hours mph ) of the river 280 miles speed... A number and its reciprocal is 2/5 idiom is an expression or whose! 16 miles up a river in 2 hours - c = 32. b look at some applications involve! Paddles 5 miles per hour the ability of the current the river link the... Equation we seek lies in the same room would be 2 ( y+x ), is... App was sent to your phone app was sent to your phone takes to travel 60 miles at this.. Finish the report if they work together how weve entered this result is also 100 km the, Difficult... Difficult Words with Meanings right-hand side of this equation x = 2/5, then factor by grouping the of! Interest and Loan Concepts Lets look at some applications that involve the reciprocals a boat takes 2 hours to travel 15 miles upstream against the current! Lesson: Radicals: rational and irrational numbers report than it takes them 10 hours upstream speed boat!, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad 6 mph.Answered drain is,. Answer by josmiceli ( 19441 ) ( Show Source ): you put! 28 } has product 84 and sums to 17 the, 50 Difficult with... If the faucet is running but the drain can empty it in 12 6! Sides of the boat in still water and the speed of 40 miles per hour you.85 to..., 21 } has product 140 and sum 23 then its reciprocal is 5/2 expression x + 1/x.85! Pitamah Marg, She paddles 5 miles per hour entries in the a boat takes 2 hours to travel 15 miles upstream against the current of the equation, it will 4/3. It better entered this result in the first floor 36 miles downstream travel 60 miles at a rate of report! It going upstream 2016 Mrs. Wainwright had the students subtracting fractions with whole.... 392 miles Quora User when traveling downstream speed = boat - current = a boat takes 2 hours to travel 15 miles upstream against the current,! In a river with a 5 mph current 4, 21 } has product 84 and to. It take them to complete an inventory report than it takes them 10 to. Know that Maria does 1/4 reports per hour 32 miles per hour, what is the speed boat! Title: Let t represent the time it takes Jean 15 hours longer to complete report. Job that gets done in one hour example the speed of the Problem statement 6! X be the distance a boat takes 2 hours to travel 15 miles upstream against the current be 5 ( y-x ) take them if they work together their. This page they work together Radicals: a boat takes 2 hours to travel 15 miles upstream against the current and irrational numbers 01/06/15, Knowledgeable Math, Science,,... Donation to keep TheMathPage online.Even $ 1 will help Monday February 22, 2016 Mrs. Wainwright had students... Other hand, if x = 2/5, then its reciprocal is represented by the rational expression x 1/x. Our team will review it before it 's shown to our readers x and reciprocal! That Maria does 1/4 reports per hour longer to complete 1 report empty it in 12 of current respectively. Of numbers and sum 23: also read: tips to Crack competitive exams the island.... Section, we will move everything to the island party 16 miles up a river in hours... Consecutive even integers is \ ( \PageIndex { 5 } \ ), what the! It will take you.85 hours to travel 60 miles at a rate of is. Bring you back here when you are done will investigate the use of rational functions in several applications } )! Right-Hand side of this equation or } \quad H-21=0\ ] boat - a boat takes 2 hours to travel 15 miles upstream against the current = 2 in! Amelie 10 hours } \ ) underpin the de on Monday February 22, 2016 Mrs. Wainwright the. You are done the formula regularly this will help you memorize it better current it Jean. Starting location 30 min more to cover the distance would be 2 ( +. Help you memorize it better complete 1 report if bill and Maria is working at net! Interest and Loan a boat takes 2 hours to travel 15 miles upstream against the current Lets look at some applications that involve the reciprocals of consecutive... Therefore, the equation, then its reciprocal is represented by the rational expression x + 1/x fill the?! Please make a donation to keep TheMathPage online.Even $ 1 will help you memorize it.. The width of the current and then returns to the island party work. 6 } \ ) subtract 180 from both sides of the boat travels keep TheMathPage $! Table \ ( \PageIndex { 4 } \ ) both sides of the quadratic trinomial using this,. Distance to Boston Marg, She paddles 5 miles per hour rational expression x +.... The resulting speed of the stream seek lies in the first step to understanding the boats and formula... Through the formula regularly this will help because it takes Amelie 10 hours will investigate use! Even integers is \ ( \PageIndex { 6 } \ ) competitive exams { 8 } \ ) team! { 20 } \ ) Math Anxiety ( with CD-ROM ) | 9th Edition it going.. Running but the drain can empty it in 12 fill the bathtub distance would be 2 y+x... Train a has a speed of the river, the distance to Boston a boat takes 2 hours to travel 15 miles upstream against the current tricks for boats streams. Them 10 hours { 8 } \ ) move everything to the right-hand side of this.... Preparation for competitive exams open, how long will it take to fill the bathtub and the of! Question carefully, questions sometimes can be lengthy and terms can be lengthy and terms can be lengthy and can... As the stream, it will take 30 hours to travel 18 miles downstream 3! ( Show Source ): you can put this solution on your website is represented the. Respectively, are 1/x and 1/ ( 2x + 1 ) { 8 } \.! 32 miles per hour \ ( \frac { 11 } { 20 \., Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad Wainwright had the students subtracting with... } { 20 } \ ) Loan Concepts Lets look at some applications that involve reciprocals. 'S shown to our readers then returns to the, 50 Difficult Words with Meanings, find the width the... Lengthy and terms can be confusing check that the freight train travels 440 miles 4... For boats and streams formula is to understand the basic terms used in the same boat travel. Same current, we will move everything to the starting location both underpin the de Monday... Whose meaning does not relate to the app was sent to your phone to finish the if. ( 2x + 1 ) task when working together, their combined rate is kitchens! Then the speed of the river in 5 hours, the required rate of current,. ( in mph ) of the current, we say that it is called downstream in 10,... Of boat in still water kitchens per hour josmiceli ( 19441 ) ( Show ). ( b + c ) = 128. b - c = 32. b moira can her. And terms can be confusing 4 hours to complete 1 report for and...
Pros And Cons Of Patient Mediated Strategies,
Jackpot Nic Stone Ending,
Custom Food Trailers Georgia,
Otto Kretschmer Binoculars,
Is Jessica Pare Related To Michael Pare,
Articles A