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

This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? Your contact details will not be published. Thus. Please make a donation to keep TheMathPage online.Even $1 will help. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. 2003-2023 Chegg Inc. All rights reserved. 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. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. 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. How many hours will it take if they work together? Boris can paddle his kayak at a speed of 6 mph in still water. Freshwater, Sydney, NSW 2096, A speedboat can travel 32 miles per hour in still water. . Find the number(s). It takes Sanjay 9 hours to paint the same room. }\]. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. The speed of a freight train is 20 mph slower than the speed of a passenger train. Note how weve entered this result in the first row of Table 6. However, they both lead to the same number-reciprocal pair. Then the speed of train B is Lets check our solution by taking the sum of the solution and its reciprocal. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? Each of these linear equations is easily solved. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Boris can paddle his kayak at a speed of 6 mph in still water. still water and the speed of the current. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. The speed of a boat in still water is 15 mi/hr. The site owner may have set restrictions that prevent you from accessing the site. The boat travels at miles per hour in still water. Solve the equation d = vt for t to obtain. To check, you can substitute these numbers back into the original problem and confirm that they are consistent with the way the problem was described. In similar fashion, the time to travel downstream is calculated with. Let's see what kinds of equations we can come up with. Find the number(s). Let's say I'm in a 10 mph current in a canoe. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. United Kingdom, EC1M 7AD, Leverage Edu Really? Problem 12. These results are entered in Table \(\PageIndex{4}\). answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. 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. Job problem. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. The second number is 1 larger than twice the first number. We know that Bill does 1/2 reports per hour. 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. 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. The same boat can travel 36 miles downstream in 3 hours. 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. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Set this equal to 29/10. Sanjay can paint a room in 5 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. Leverage Edu wishes you all the best for all your future endeavors. An amusement park sold 6 4/5 gallons of soda. If they work together, it takes them 3 hours. 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 How tall is the tower? Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. The speed of a boat in still water is 15 mi/hr. In one hour, a boat goes 11 km along the stream and 5 km against the stream. What are the speed of the boat in still water and the speed of the stream? Rate problems are based on the relationship Distance As a result of the EUs General Data Protection Regulation (GDPR). It will take 30 hours to travel 60 miles at this rate. 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. The speed of the current is 5 miles per hour. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. How much time will it take to come back? Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. The same boat can travel 36 miles downstream in 3 hours. Problem 13. where d represents the distance traveled, v represents the speed, and t represents the time of travel. If the boat is traveling A boat takes 2 hours to travel 15 miles upriver against the current. Get a free answer to a quick problem. Multiple Subject Credential Program 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? For Free. Example 4. The speed of the boat in still water is 3 miles per hour. Weve also added this entry to the time column in Table \(\PageIndex{2}\). 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 sum of a number and its reciprocal is \(\frac{41}{20}\). Below is the equation to convert this number into minutes. Find the two numbers. Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. Find the speed of the current and the speed of the boat in still water. Most questions answered within 4 hours. rate and time that the boat travels going both upstream and downstream. Each of these things will Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). 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? 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. What is the speed of the boat in still water? The speed of a freight train is 19 mph slower than the speed of a passenger train. . 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Every applicant should memorize these and should be on fingertips. A boat can travel 24 miles in 3 hours when traveling with a current. Find the two numbers. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Lesson Plan We are not permitting internet traffic to Byjus website from countries within European Union at this time. Thus, Bill is working at a rate of 1/2 report per hour. Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. Let x represent the first number. Mr. Larlham This will take 150/24 or 6.25 hours. How long it takes the faster one. The hiker walks 8 miles north, and then 6 miles east. Junior's boat will go 15 miles per hour in still water. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. There are two numbers. Example 3. Answer: 1 hour 15 minutes. Besides testing the ability of the student, exams are important. Problem 6. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . Again, it is very important that we check this result. How far away was Boston? 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. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions A man has painted 1/5 of a tower. The key to this type of problem is: What fraction of the job gets done in one hour? Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. That is, if x = 5/2, then its reciprocal is 2/5. When a boat travels in the same direction as the current, we say that it is traveling downstream. it will become 12 = B+C. 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. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. per hour. That will give the equation. If we divide both sides of the first equation by 2, it We'll put this information in our chart: Each row in the chart will give us an equation. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). Jean can paint a room in 4 hours. Find the speed of the current. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. How many hours would it take Amelie if she worked alone? Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. Then the speed of the car is Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. If the faucet is running but the drain is open, how long will it take to fill the bathtub? The resulting speed of the boat (traveling downstream) Break up the middle term using this pair and factor by grouping. Distance = Speed Time It takes Amelie 9 hours to paint the same room. Here is the equation: Problem 11. The boat goes along with the stream in 5 hours and 10 minutes. by Martynabucytram11, The total time of the trip is 6 hours. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. Emily can paddle her canoe at a speed of 2 mph in still water. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). __________________ 3. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. A boat can travel 16 miles up a river in 2 hours. The speed of this stream (in km/hr) will be: [RRB 2002] A) 4 B) 5 C) 6 D) 10 E) None of these Q3: The speed of a boat in still water is 10 km/hr. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). The last part of the equation is to subtract the travel time by boat from the time the party starts. to work with: The speed of the current is 2 miles per hour. A boat can travel 16 miles up a river in 2 hours. We have advice similar to that given for distance, speed, and time tables. A link to the app was sent to your phone. . To clear fractions from this equation, multiply both sides by the common denominator 10x. Choose an expert and meet online. 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. The rate of the current is 15 km/hour and the . Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. then the time taken by the boat to travel 100 km with the current is? \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Sophie Germain was born in Paris, France on April 1, 1776. A boat can travel 24 miles in 3 hours when traveling with a current. Expand, simplify, make one side zero, then factor. 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 The quantitative section covering boat and stream questions doesnt contain the same type of questions. that distance. If the speed of the boat in still water is 10 mph, the speed of the stream is: Together, they can complete the same job in 12 hours. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. 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. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Expand and simplify each side of this result. a. The total time of the trip is 10 hours. Now let's think about the rate the boat travels. When a boat travels against the current, it travels upstream. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. 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? Find the rate of the current and the rate of the boat in still water. so we have 2 equations which must be solved . x15. At last, practice makes the students perfect. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment 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? However, there is variation in questions that demands more variation in formulas as well. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. 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. Moira can paddle her kayak at a speed of 2 mph in still water. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. (Each 1/12 of an hour is 5 minutes so that down stream trip takes 25 minutes) Thus, total trip by this calculation takes 1 hour and 40 minutes, not the stated 1.5 hours. In this direction, the current works WITH the boat's engine, so the rate would be y + x. our information in it: A boat can travel 16 miles up a river in 2 hours. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). 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. The speed of a freight train is 16 mph slower than the speed of a passenger train. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. It takes Bill 2 hours to complete 1 report. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. In general, if a job takes x hours, then in one hour, will get done. Here's what the chart looks like before we put any of Raymond can do a job in 3 hours, while it takes Robert 2 hours. First, let us explain the meaning of "upstream" and "downstream.". The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Get a free answer to a quick problem. This leads to the entries in Table \(\PageIndex{7}\). Find the two numbers. Because distance, speed, and time are related by the equation d = vt, whenever you have two boxes in a row of the table completed, the third box in that row can be calculated by means of the formula d = vt. Carlos can do a certain job in three days, while it takes Alec six days. That is, the second number is 5. The total time of the trip is 9 hours. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). The key to this type of problem is same time. the boat, and the boat's speed will decrease by C miles per hour. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! Is it something that matters in the preparation for competitive exams? Our team will review it before it's shown to our readers. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. What is the speed of the boat in still-water, and how fast is it in the current? Required fields are marked *. Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. Jacob is canoeing in a river with a 2 mph current. Always go through the formula regularly this will help you memorize it better. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Find the number(s). Solution. Introducing Cram Folders! \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. Solution. The rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. It will . Here is the guiding principle. Problem 9. .85 x 60 (minuntes in 1 hour) = 50 minutes. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . The return trip 2 hours going downstream. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. This problem ask the students to use division to solve the problem and they were not able to do that. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. We'll put 36 in our chart for the distance downstream, and we'll put 3 Hence, we want to isolate all terms containing c on one side of the equation. it's moving upstream and downstream on a river. The sum of a number and its reciprocal is \(\frac{5}{2}\). On the other hand, if x = 2/5, then its reciprocal is 5/2. is B+C miles per hour. It can go 24 mile downstream with the current in the same amount of time. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? A woman deposits $600 into an account that pays 5 1/4 interest per year. Two people working together can complete a job in six hours. 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. That is, Bill will complete 2/3 of a report. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. What is the rate of water's current? That is, Maria will complete 1/3 of a report. 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). 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