A boat can travel 16 miles up a river in 2 hours. The sum of a number and its reciprocal is 29/10. }\]. A boat takes 2 hours to travel 15 miles upriver against the current. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. For Free. \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. End-to-end support for your study abroad journey. If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water. This leads to the entries in Table \(\PageIndex{7}\). The rate of the current is 15 km/hour and the . The speed of the boat in still water is Medium View solution > Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Note that we simply invert the number 3 to obtain its reciprocal 1/3. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. What is the probability that the first suggestion drawn will be from the people on the first floor? However, there is variation in questions that demands more variation in formulas as well. In one hour, a boat goes 11 km along the stream and 5 km against the stream. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). How tall is the tower? Find out how you can intelligently organize your Flashcards. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Solving the system of equations simultaneously, we get. The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. we need to write our two equations. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. 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. We can calculate the rate at which Hank is working alone by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substituting Hanks data from row one of Table \(\PageIndex{7}\). Find the two numbers. A boat takes 2 hours to travel 15 miles upriver against the current. Expand and simplify each side of this result. Lets try to use the ac-test to factor. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 9 miles downstream, what is the speed of the current? In general, if a job takes x hours, then in one hour, will get done. We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. The total time of the trip is 10 hours. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. We still need to answer the question, which was to find two numbers such that the sum of their reciprocals is 7/10. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. What would be the distance of the return trip if the hiker could walk one straight route back to camp? x30. For example, if a job takes 3 hours, then in one hour, will get done. 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. at a rate of B miles per hour. The speed of a boat in still water is 30 mph. answered 02/17/15, Olubunmi B. in the chart for the time downstream. = (Rate)(Time). This problem ask the students to use division to solve the problem and they were not able to do that. At last, practice makes the students perfect. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. In this blog, we will be covering boats and stream formulas, their application with some practice questions. Geometry Project- 6 This is an alternate ISBN. Solution. Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. Leverage Edu Tower, Then is that fraction of the job that gets done in one hour. What is the rate of water's current? Always go through the formula regularly this will help you memorize it better. Choose an expert and meet online. Find the speed of the freight train. If they work together, it takes them 3 hours. It can go 24 mile downstream with the current in the same amount of time. What is the speed of the current of the river? What is the speed (in mph) of the current? 5 May 2016 Because the total time to go upstream and return is 10 hours, we can write. Moira can paddle her kayak at a speed of 2 mph in still water. 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). A student gave 2/3 of her cassette tapes to her friend. 2700 = ________________ 4. How many hours would it take Sanjay if he worked alone?
Example 5. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. The speed of the current is miles per hour. For Free. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. 1. 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. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. what is the speed of the boat in still water and of the current river? 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. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. How much time will it take to come back? be represented by a different variable: Since we have two variables, we will need to find a system
What are the speed of the boat in still water and the speed of the stream? Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. What is the speed of the current in miles per hour. Here's what the chart looks like before we put any of
This will take 150/24 or 6.25 hours. 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 merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Sophie Germain was born in Paris, France on April 1, 1776. To find the speed of the current, we can substitute 10
The key to this type of problem is same time. . Break up the middle term using this pair and factor by grouping. 2(b + c) = 128. b - c = 32. b . To organize our work, we'll make a chart of the distance,
Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions However, as we saw above, the rates at which they are working will add. 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. Each of these things will
These results are entered in Table \(\PageIndex{4}\). 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? Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). What is the speed of the boat in still water? Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). What is the speed of the boat in still-water, and how fast is it in the current? An amusement park sold 6 4/5 gallons of soda. When a boat travels against the current, it travels upstream. A-258, Bhishma Pitamah Marg, Block A, To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. There are two numbers. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. It is important to check that the solution satisfies the constraints of the problem statement. A link to the app was sent to your phone. Train A has a speed 15 mi/hr greater than train B. More answers below Quora User Making educational experiences better for everyone. If she kept 24 tapes, how many did she give away? So, your trip will take 50 minutes from your dock to the island. Find the speed of the current and the speed of the boat in still water. 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 It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. Find the speed of the freight train. As a result of the EUs General Data Protection Regulation (GDPR). Note that each row of Table \(\PageIndex{1}\) has two entries entered. 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. Answer: 1 hour 15 minutes. Find the two numbers. not flowing then the speed of water is zero. where d represents the distance traveled, v represents the speed, and t represents the time of travel. The sum of a number and its reciprocal is \(\frac{41}{20}\). Find the number(s). 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. The boat goes along with the stream in 5 hours and 10 minutes. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. A painter can paint 4 walls per hour. Find the two numbers. Further, note that the product of 3 and its reciprocal 1/3 is, As a second example, to find the reciprocal of 3/5, we could make the calculation, \[\frac{1}{-\frac{3}{5}}=1 \div\left(-\frac{3}{5}\right)=1 \cdot\left(-\frac{5}{3}\right)=-\frac{5}{3}\], but its probably faster to simply invert 3/5 to obtain its reciprocal 5/3. On your markGet setMental Math Madness! Find the two numbers. 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). Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. You will only be able to solve these questions if you have memorized the boats and streams formula. We weren't able to detect the audio language on your flashcards. What proportion of the kites are blue? so we have 2 equations which must be solved . If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. Find the speed of the freight train. Let c represent the speed of the current. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 The speed of a freight train is 19 mph slower than the speed of a passenger train. A boat takes 1.5 hour to go 12 mile upstream against the current. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. To clear fractions from this equation, multiply both sides by the common denominator 10x. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Problem 9. Solution. She paddles 5 miles upstream against the current and then returns to the starting location. Find the speed of the current and the speed of the boat in still water. What is the speed of the current? Emily can paddle her canoe at a speed of 2 mph in still water. A chef mixes his salt and pepper. A hiker follows a trail that goes from camp to lake. It will take 30 hours to travel 60 miles at this rate. Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. The same boat can travel 36 miles downstream in 3 hours. The same boat can travel 36 miles downstream in 3 hours. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. A boat can travel 24 miles in 3 hours when traveling with a current. In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . It takes Maria 4 hours to complete 1 report. Jon P. The sum of a number and its reciprocal is \(\frac{5}{2}\). That is, Bill will complete 2/3 of a report. The speed of the boat (in still water) is 13 miles/hour. For in one hour, Raymond does of the job, and Robert, . our information in it: A boat can travel 16 miles up a river in 2 hours. 19 . Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. Find the speed of the current. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Find the rate of the current and the rate of the boat in still water. Let x be the speed of the train. 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. Lets look at another application of the reciprocal concept. We have advice similar to that given for distance, speed, and time tables. His speed of the boat in still water is 3 km/hr. Signature Assignment for EDEL 462 The passenger train travels 440 miles in the same time that the freight train travels 280 miles. The hiker walks 8 miles north, and then 6 miles east. The return trip 2 hours going downstream. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. 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 \(\PageIndex{5}\). How long does it take him to go 5 km in stationary water? Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. No packages or subscriptions, pay only for the time you need. A boat takes 2 hours to travel 15 miles upriver against the current. for the B in any of our equations. that distance. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Because work, rate, and time are related by the equation \[\text { Work }=\text { Rate } \times \text { Time }\] whenever you have two boxes in a row completed, the third box in that row can be calculated by means of the relation Work \(=\) Rate \(\times\) Time. In downstream it takes 3 hours to travel 36 km. Choose an expert and meet online. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Add to folder The total time of the trip is 5 hours. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. Problem 13. Let's say I'm in a 10 mph current in a canoe. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. The total time of the trip is 9 hours. Please make a donation to keep TheMathPage online.Even $1 will help. 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. The boat travels at miles per hour in still water. How long will it take them if they work together? Solution. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. . Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. We will move everything to the right-hand side of this equation. Problem 12. A boat can travel 24 miles in 3 hours when traveling with a current. The resulting speed of the boat (traveling upstream) is B-C miles per hour. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Distance = Speed Time How long will it take them to finish the report if they work together? distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down Find the two numbers. The speed of a boat in still water is 15 mi/hr. Carlos can do a certain job in three days, while it takes Alec six days. 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? 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. All rights reserved. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. }\], A second important concept is the fact that rates add. If the current in the river is 3 miles per hour, find the speed of the boat in still water. It will take 30 hours to travel 60 miles at this rate. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. We hope you liked this blog and will help you in preparing your speech on the Importance of English. 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). How many hours will it take if they work together? The sum of the reciprocals of the two numbers is 7/10. A man has painted 1/5 of a tower. . 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 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. 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 see what kinds of equations we can come up with. Making educational experiences better for everyone. 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. Then the speed of boat in still water and the speed of current are respectively. 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. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). Total time problem. How many hours will it take if they work together? A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. Thus, Bill is working at a rate of 1/2 report per hour. Below is the equation to convert this number into minutes. The total time of the trip is 6 hours. Step-by-step solution Chapter 2.2, Problem 85P is solved. Together, they can complete the same job in 12 hours. How many miles are represented by 6 inches? 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. still water and the speed of the current. Legal. 3 . Get a free answer to a quick problem. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. A boat travels 30 miles upstream in 5 hours. What was the interest rate on the loan? Find the rate of the current and the rate of the boat in still water. For example, in the first row, d = 60 miles and v = 3 c miles per hour. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. 2003-2023 Chegg Inc. All rights reserved. Hence, we want to isolate all terms containing c on one side of the equation. whereas when traveling upstream it is 28 km/hr. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Solution. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! Our chart now looks like . __________________ 3. Same time problem: Upstream-Downstream. Please select the correct language below. A boat takes 2 hours to travel 15 miles upriver against the current. . (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? A link to the app was sent to your phone. We'll choose the easiest equation
What is the speed (in mph) of the current? Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. She paddles 3 miles upstream against the current and then returns to the starting location. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. The integer pair {5, 28} has product 140 and sum 23. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Your contact details will not be published. It takes Bill 2 hours to complete 1 report. Also Read: A Guide On How to Prepare for Bank Exams. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). Let x be how long will it take them if they work together. So after 2 hours, the distance would be 2(y+x), which is also 100 km. The sum of a number and twice its reciprocal is \(\frac{9}{2}\). Solve the equation d = vt for t to obtain. Introducing Cram Folders! Note that the product of a number and its reciprocal is always equal to the number 1. 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. The last part of the equation is to subtract the travel time by boat from the time the party starts. What is
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? Here is a useful piece of advice regarding distance, speed, and time tables. It will . Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. No packages or subscriptions, pay only for the time you need. Get a free answer to a quick problem. 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. We'll put 16 in our chart for the distance upstream, and we'll put 2 in
However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. 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? 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 many hours will it take if they work together? { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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