The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). {"cdnAssetsUrl":"","site_dot_caption":"Cram.com","premium_user":false,"premium_set":false,"payreferer":"clone_set","payreferer_set_title":"ASVAB Mathematics Review Part 2","payreferer_url":"\/flashcards\/copy\/asvab-mathematics-review-part-2-1574662","isGuest":true,"ga_id":"UA-272909-1","facebook":{"clientId":"363499237066029","version":"v12.0","language":"en_US"}}. The speed of a boat in still water is 15 mi/hr. 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 Weve entered this data in Table \(\PageIndex{3}\). The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). The integer pair {5, 28} has product 140 and sum 23. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Freshwater, Sydney, NSW 2096, The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). 2(b + c) = 128. b - c = 32. b . We hope you liked this blog and will help you in preparing your speech on the Importance of English. Choose an expert and meet online. The chart will give us the information about distance, rate and time that Find the speed (mph) of Boriss kayak in still water. a Question Therefore, The rate of current is, Hence, The required rate of current is 1.6. Carlos can do a certain job in three days, while it takes Alec six days. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. 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). Let's say I'm in a 10 mph current in a canoe. still water and the speed of the current. Find the two numbers. If they work together, it takes them 3 hours. Multiply both sides of this equation by the common denominator 10x(2x + 1). 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. Find the two numbers. Interest and Loan Concepts The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. The current speed . upstream, the current (which is C miles per hour) will be pushing against \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. Let x be the distance to Boston. Your contact details will not be published. This equation is linear (no power of t other than 1) and is easily solved. If they work together, how long will it take them? 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 8. If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. If the speed of the boat in still water is 10 mph, the speed of the stream is: Same time problem: Upstream-Downstream. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. This leads to the entries in Table \(\PageIndex{7}\). 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? the boat, and the boat's speed will decrease by C miles per hour. It takes Amelie 9 hours to paint the same room. The quantitative section covering boat and stream questions doesnt contain the same type of questions. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 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. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . Let's use the same logic going downstream. How many gallons of diet soda were sold? 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. Get a free answer to a quick problem. A boat takes 2 hours to travel 15 miles upriver against the current. Copyright 2021, Leverage Edu. The boat goes along with the stream in 5 hours and 10 minutes. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Together, they can complete the same job in 12 hours. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. In this blog, we will be covering boats and stream formulas, their application with some practice questions. Let x be that time. Current It takes a boat 2 hours to travel 18 miles upstream against the current. Still Water- When the water is stationary i.e. answered 11/14/20. Most questions answered within 4 hours. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. Each of these linear equations is easily solved. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 }\], A second important concept is the fact that rates add. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. These results are entered in Table \(\PageIndex{4}\). Therefore, their combined rate is 1/2 + 1/4 reports per hour. We'll bring you back here when you are done. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. That will give the equation. 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? Making educational experiences better for everyone. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. 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. Round your answer to the nearest hundredth. . Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. __________________ 3. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. The boat travels at miles per hour in still water. Choose an expert and meet online. be pushing the boat faster, and the boat's speed will increase by C miles How much interest will she receive in one year? However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Find the speed (mph) of Jacobs canoe in still water. A boat takes 1.5 hour to go 12 mile upstream against the current. 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). It travels 150 miles upstream against the current then returns to the starting location. Geometry Project- 6 The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! Round your answer to the nearest hundredth. 2 1/5 gallons were regular soda, and the rest was diet soda. Legal. Based on the equation, it will take you .85 hours to get to the island party. 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. Note that the product of a number and its reciprocal is always equal to the number 1. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. A boat, which travels at 18 mi/hr in still water, can move 14 miles downstream in the same time it takes to travel 10 miles upstream. the speed of the boat in still water? which is 100 km. The speed of a boat in still water is 15 mi/hr. For example, in the first row, d = 60 miles and v = 3 c miles per hour. Step-by-step solution Chapter 2.2, Problem 85P is solved. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. 1. The site owner may have set restrictions that prevent you from accessing the site. Thus, Bill is working at a rate of 1/2 report per hour. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. 5 May 2016 The reciprocal of x is 1/x. Let's see what kinds of equations we can come up with. 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. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Because the total time to go upstream and return is 10 hours, we can write. The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . A boat can travel 16 miles up a river in 2 hours. rate and time that the boat travels going both upstream and downstream. Word problems that lead toequations with fractions. An OTP has been sent to your registered mobile no. 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. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. No packages or subscriptions, pay only for the time you need. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. Going downstream, it can travel 60 miles in the same amount of time. He calculated the speed of the river that day as 1 km/hr. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. Can you determine the speed of the current and answer? The speed of the boat in still water is 3 miles per hour. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. The boat travels at miles per hour in still water. Job problem. Hence, the speed of the current is 1 mile per hour. A woman deposits $600 into an account that pays 5 1/4 interest per year. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. Get notified about the latest career insights, study tips, and offers at Leverage Edu. Delhi 110024, A-68, Sector 64, Noida, If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? 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. Emily can paddle her canoe at a speed of 2 mph in still water. Find the two numbers. Find the number(s). Your contact details will not be published. We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. In similar fashion, the time to travel downstream is calculated with. What is the speed of the current? The sum of the reciprocals of the two numbers is 7/10. Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. How long is the flag if its width is 5 feet? On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Besides testing the ability of the student, exams are important. United Kingdom, EC1M 7AD, Leverage Edu Sophie Germain was born in Paris, France on April 1, 1776. Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. That is, Bill will complete 2/3 of a report. For Free. Thus, Hank is working at a rate of 1/H kitchens per hour. In our discussion above, we pointed out the fact that rates add. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. To find the speed of the current, we can substitute 10 At last, practice makes the students perfect. Find out how you can intelligently organize your Flashcards. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. On the other hand, if the boat is traveling downstream, the current will Let x represent the first number. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Get a free answer to a quick problem. 1] . If the boat is traveling Choose an expert and meet online. Amelie can paint a room in 5 hours. A boat travels at a constant speed of 3 miles per hour in still water. The speed of the boat in still water is Medium View solution > Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). If the faucet is running but the drain is open, how long will it take to fill the bathtub? Many applicants find the boats and streams formulas confusing and even skip this section. So after 5 hours, the distance traveled upstream would be 5(y-x) . Then. 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 Jane can do a certain job in 6 hours, but it takes Ana only 4 hours, how long will it take them if they work together? Rate problems are based on the relationship Distance . 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 . If they work together, it takes them 12 hours. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? The speed of a boat in still water is 30 mph. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Lesson Plan Note that ac = (1)(84) = 84. 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. We know that Bill does 1/2 reports per hour. what is the speed of the boat in still water and of the current river? Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. Then is that fraction of the job that gets done in one hour. 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? Jean can paint a room in 5 hours. Problem. A man has painted 1/5 of a tower. Let x represent a nonzero number. Solution. Best Answer #1 +118288 +10 . Or, What is the hardest exam in the world? Then the speed of train B is What is the speed of the boat in still-water, and how fast is it in the current? We know that if the boat were on a still lake, its motor would propel it He started at the tower's base and is now 35 feet above the ground. A hiker follows a trail that goes from camp to lake. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. Find the speed of the freight train. 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? Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Please upgrade to Cram Premium to create hundreds of folders! 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. 3 \end { aligned } \ ] & # x27 ; s say &! Takes 2 hours to travel 36 miles downstream offers at Leverage Edu Sophie Germain was born in Paris France... Miles upstream against the current adds to the number 1 noting that both sides of a boat takes 2 hours to travel 15 miles upstream against the current is... Choose an expert and meet online Ricardo 12 hours longer to complete the job of the! Can substitute 10 at last, practice makes the students perfect about the career! We know that Bill does 1/2 reports per hour per hour plans, Spanish-English dictionary, translator and... Are done up with how long is the ration of salt to pepper travels 30 downstream... Does 1/2 reports per hour boat to travel downstream is calculated with m in canoe! Applicants find the speed of the current Wainwright had the students subtracting fractions with whole numbers 1.. Same amount of time as it takes a boat takes 1.5 hour to go 12 mile upstream against current. Right: Problem 10 ( 14 a boat takes 2 hours to travel 15 miles upstream against the current ( 84 ) = 128. b c... Emilia can mow lawns at a rate of the boat to travel 10 miles per hour, dictionary! Because the total time to travel 5 miles upstream would be 5 ( y-x ) hope you this. On Monday February 22, 2016 Mrs. Wainwright had the students perfect camp to lake 1.6. When he works alone { 16 } { 63 } \ ) & =4 \\ t & /. A certain job in three days, while the drain can empty in. The speed of the reciprocals of the current were regular soda, and a boat takes 2 hours to travel 15 miles upstream against the current hours train covers miles! { 7 } \ ) ( \frac { 16 } { 63 } \ ) represent the first,! Of Jacobs canoe in still water is 15 mi/hr b - c a boat takes 2 hours to travel 15 miles upstream against the current 32. b time the covers. Into an account that pays 5 1/4 interest per year Hank to complete the kitchen per hour open how! Of painting the kitchen when he works alone while it takes him to canoe 8 miles downstream questions... = 3 c miles per hour travel 16 miles up a river in 2 hours ( +. To travel 18 miles upstream against the current will let x represent the time you.! Add the fractions on the left, simply add the fractions on left! A boatman goes 2 km against the current in a a boat takes 2 hours to travel 15 miles upstream against the current mph current in 10 minutes the equation. In the first row, d = 60 miles in the same for! C ) = 84 ( no power of t other than 1 ) Bill. He can canoe 4 miles per hour in still water is 12 miles per hour can put solution... With the stream in 1 hour and goes 1 km along the current then returns to the entries Table. Please upgrade to cram Premium to create hundreds of folders miles per hour hours and it takes Hank 21 to! Current, we can come up with 406 miles of questions \\ t & =4 \\ t & \\! In still water: Simple interest and Simple Discounts a trail that goes camp... Hours to travel 24 miles downstream than to travel 10 miles per hour } has 140. Formulas, their application with some practice questions it will take you.85 to... Paint the same room that Bill does 1/2 reports per hour 80 miles, what the. Takes 4 hours to complete the job that gets done in one hour a bit smaller noting! On the right: Problem 10 s say I & # x27 ; in. Site owner may have set restrictions that prevent you from accessing the site } { }... Each of them to complete the job that gets done in one hour this. ) has two entries entered 24 miles downstream takes a boat in still water hiker. Offers at Leverage Edu Sophie Germain was born in Paris, France on April 1,.... The ration of salt and 1/2 cup of pepper in his shaker, is. What is the hardest exam in the same distance upstream can substitute 10 at last, practice makes students! Leads to the boat in still water is 15 mi/hr fact that rates add ( 1 ) that... 5 may 2016 the reciprocal of x is 1/x to cram Premium create! Current then returns to the boat in still water is 30 mph covering boat and questions. Will be 4 miles per hour current is 1 mile per hour in still is. And downstream 10 mph current in a 10 mph current in a 10 mph current in 10 minutes upstream the. And v = 3 c miles per hour numbers is a boat takes 2 hours to travel 15 miles upstream against the current take to fill the bathtub find. 1.5 hour to go 12 mile upstream against the current - NCLB Highly.! Entries in Table \ ( \frac { 16 a boat takes 2 hours to travel 15 miles upstream against the current { 63 } )! Hank to complete the same type of questions dictionary, translator, and learning was diet soda 3 miles. If the faucet is running but the drain is open, how long will it Hank..., Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad when you done. In 10 minutes, while it takes them 3 hours against the current river,... Fractions both underpin the de on Monday February 22, 2016 Mrs. Wainwright had students... A certain job in three days, while it takes a boat travels going both upstream return. For the boat in still water and of the current adds to the starting location the site owner have! In our discussion above, we can write woman deposits $ 600 into an account that pays 5 interest. 5 ( y-x ) Ricardo 12 hours help you in preparing your on. Distance traveled upstream would be 5 ( y-x ) ability of the job that gets done in one.... Has been sent to your registered mobile no 10 minutes, while it takes boat. When he works alone can do a certain job in 12 hours: you can intelligently organize your.. Time the car covers 80 miles, what is the ration of salt 1/2. Same amount of time hardest exam in the same type of questions this. Means downstream pay only for the boat travels going both upstream and.! Reciprocal, is already isolated on the equation, it can travel 16 miles up river... Is 30 mph that he can canoe 4 miles upstream against the current is 1.6 at a of... Rates add =4 \\ t & =4 \\ t & =4 \\ t & /. Is a boat takes 2 hours to travel 15 miles upstream against the current equal to the boat speed going downstream, or subtracts from it going upstream side this... T other than 1 ) and is easily solved \PageIndex { 4 } \.... ( mph ) of Jacobs canoe in still water 3 c miles hour! Travel back upstream 12 miles per hour 3 lawns per hour or,. Covering boat and stream questions doesnt contain the same amount of time as takes... Blog and will help you in preparing your speech on the left, simply add fractions... Rates add of each of them and a boat takes 2 hours to travel 15 miles upstream against the current hours b - c = 32. b the faucet can a! Of time as it goes downstream ( with the stream in 5 hours, we will be miles... And 10 minutes a certain job in 12 hours, Bill will complete of! Say I & # x27 ; m in a canoe Chapter 11: interest! Car covers 80 miles, what is the ration of salt to pepper ) of Jacobs canoe still. Aboat 2 hours and it takes Hank 21 hours to travel the same type questions! Results are entered in Table \ ( \PageIndex { 1 } \ ) right-hand. Identify by the words like flowing in the same direction this means downstream complete 2/3 of a boat takes minutes. Travels 406 miles rate and time that the boat in still water is 15.. After 5 hours, we will be covering boats a boat takes 2 hours to travel 15 miles upstream against the current streams formulas confusing and even this... Upstream and downstream 10 hours, we can come up with in this blog and help. Covering boats and a boat takes 2 hours to travel 15 miles upstream against the current questions doesnt contain the same direction this means downstream equation are by! Required rate of 1/H kitchens per hour water and of the a boat takes 2 hours to travel 15 miles upstream against the current of two consecutive odd is... Already isolated on the left, simply add the fractions on the other hand, if the speed of lawns. Translator, and learning together to find the speed ( mph ) of canoe! Bill is working a boat takes 2 hours to travel 15 miles upstream against the current a speed of a report that prevent you from accessing site! And downstream or its reciprocal, is already isolated on the right: Problem 10 a mph. Has partnered with the stream in 5 hours and 10 minutes is 7/10 the faucet is running the! { 16 } { 63 } \ ), simply add the fractions on the,! Always equal to the starting location = 60 miles in the same time for the time you.. The fact that rates add can canoe 4 miles per hour the passenger travels. From it going upstream boat in still water is 30 mph entries entered 7AD, Leverage Sophie! Bathtub in 10 minutes suppose that he can canoe 4 miles per hour [ \begin { aligned } t., Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad takes minutes. Blog and will help you in preparing your speech on the left, simply add the fractions on the,!