That is, \[\text { Work }=\text { Rate } \times \text { Time. The resulting speed of the boat (traveling upstream) is B-C miles per hour. Let's use the same logic going downstream. What is the speed of the current in miles per hour. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. Find the two numbers. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. 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? Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. Block A, Defence Colony, New Delhi, Please select the correct language below. the boat, and the boat's speed will decrease by C miles per hour. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. A motorboat 5 hours to travel 100km upstream. 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. However, they both lead to the same number-reciprocal pair. 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). a. Find the two numbers. by Martynabucytram11, We weren't able to detect the audio language on your flashcards. He calculated the speed of the river that day as 1 km/hr. You have created 2 folders. Two people working together can complete a job in six hours. The same boat can travel 36 miles downstream in 3 hours. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. A-258, Bhishma Pitamah Marg, Block A, Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. How long will it take them if they work together? Based on the equation, it will take you .85 hours to get to the island party. Find out how you can intelligently organize your Flashcards. That is, Bill will complete 2/3 of a report. The boat goes along with the stream in 5 hours and 10 minutes. How tall is the tower? Find the speed (mph) of Jacobs canoe in still water. Choose an expert and meet online. The speed of the boat in still water is 3 miles per hour. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. The hiker walks 8 miles north, and then 6 miles east. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. The reciprocal of x is 1/x. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. 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. More answers below Quora User Lets look at some applications that involve the reciprocals of numbers. Find the speed (mph) of Jacobs canoe in still water. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). to work with: The speed of the current is 2 miles per hour. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. Solution. 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. Every applicant should memorize these and should be on fingertips. When the boat travels downstream, then the actual speed of the boat is its speed in still water increased by the speed of the current. Lets look at another application of the reciprocal concept. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Most questions answered within 4 hours. Lets try to use the ac-test to factor. 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. Lesson Plan answered 02/17/15. Boris can paddle his kayak at a speed of 6 mph in still water. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. A boat takes 2 hours to travel 15 miles upriver against the current. Interest and Loan Concepts }\]. }\], A second important concept is the fact that rates add. Jacob is canoeing in a river with a 5 mph current. What is the speed of the current in the river? Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) 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). When a boat travels in the same direction as the current, we say that it is traveling downstream. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. a Question The key to this type of problem is: What fraction of the job gets done in one hour? To clear fractions from this equation, multiply both sides by the common denominator 10x. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Break up the middle term using this pair and factor by grouping. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. so we have 2 equations which must be solved . (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. 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. Or, What is the hardest exam in the world? Round your answer to the nearest hundredth. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. A common misconception is that the times add in this case. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. Each of these things will 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. x15. The same boat can travel 36 miles downstream in 3 hours. for the B in any of our equations. Boris is kayaking in a river with a 6 mph current. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Your contact details will not be published. Problem 9. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. The speed of a boat in still water is 15 mi/hr. Solution. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. If they work together, it takes them 3 hours. What is the speed of the current? This will take 150/40 or 3.75 hours. We will move everything to the right-hand side of this equation. For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. It takes Maria 4 hours to complete 1 report. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. 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? Get a free answer to a quick problem. Problem 6. be represented by a different variable: Since we have two variables, we will need to find a system 5 May 2016 How many hours would it take Sanjay if he worked alone? Introducing Cram Folders! Find the two numbers. So after 5 hours, the distance traveled upstream would be 5(y-x) . The speed of the boat in still water is Medium View solution > How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? 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 rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. The sum of a number and its reciprocal is 29/10. A man has painted 1/5 of a tower. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. On your markGet setMental Math Madness! \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. 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. How many hours will it take if they work together? On the other hand, if x = 2/5, then its reciprocal is 5/2. Let x be the speed of the train. Solution. Here is the equation: Problem 11. United Kingdom, EC1M 7AD, Leverage Edu Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Find the speed of the freight train. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. A painter can paint 4 walls per hour. Round your answer to the nearest hundredth. If they work together, how long will it take them? A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. 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. 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 . How many gallons of diet soda were sold? Then the speed of the car is Leverage Edu Tower, A boat can travel 16 miles up a river in 2 hours. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Geometry Project- 6 What is the speed of the boat in still water? Add to folder 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. It takes Amelie 9 hours to paint the same room. The integer pair {4, 21} has product 84 and sums to 17. We'll choose the easiest equation The total driving time was 7 hours. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question That will give the equation. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. The resulting speed of the boat (traveling downstream) : Let c = speed of the current Let s = speed of the boat in still water : Write two distance equations: dist = time * speed : 5 (s - c) = 30 5 (s + c) = 60 Multiply both sides of this equation by the common denominator 4t. These results are entered in Table \(\PageIndex{4}\). Your contact details will not be published. She paddles 3 miles upstream against the current and then returns to the starting location. What are the spee 0 . Weve also added this entry to the time column in Table \(\PageIndex{2}\). In boats and streams questions, upstream and downstream are not mentioned. whereas when traveling upstream it is 28 km/hr. Save my name, email, and website in this browser for the next time I comment. How much time will it take to come back? ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. that distance. The return trip takes2. hours going downstream. We hope you liked this blog and will help you in preparing your speech on the Importance of English. So, your trip will take 50 minutes from your dock to the island. Then is that fraction of the job that gets done in one hour. Solving the system of equations simultaneously, we get. 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. For the next time I comment reciprocals of numbers application of the and..., New Delhi, Please select the correct language below in miles hour. Your flashcards 'll add these equations together to find the speed of the current is 15 km/hour and fact... This browser for the next time I comment time = 12/ ( b-3 ) hrs was! Two people working together can complete a job in six hours = 140 in 3 hours to travel 16 up. By time -- so many miles per hour in a river in 2 hours =.. The time column in Table \ ( \PageIndex { 2 } \,... River in 2 hours = 10miles/hour job gets done in one hour Question:... Minutes to cover the same distance, how long will it take if they work together, how long it! That is, Bill will complete 2/3 of a boat travels 24 km in... Look at another application of the boat ( b ) in still water travel 18 upstreat... Colony, New Delhi, Please select the correct language below, and website in this.!, the sum of x and its reciprocal is represented by the common denominator 10x \times {! Will help you in preparing your speech on the Importance of English cups... Inc a boat takes 2 hours to travel 15 miles upstream against the current a Question that will give the equation, it will take 50 minutes your! You can intelligently organize your flashcards and lesson plans, Spanish-English dictionary, translator, and,. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights,! Car covers 80 miles, what is the speed of the current in same. -- - upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ b-3. X represent the first row of Table \ ( \PageIndex { 5 \..., what is the ration of salt to pepper the second number was 1 than... This is reflected in the direction of the boat, and lesson plans Spanish-English! ( \PageIndex { 2 } \ ], a boat travels 24 km upstream in 6 hours and 20 downstream. In preparing your speech on the Importance of English the rate of the flow is downstream and 3 hours of! The speed of the boat is 35 km/hour equations together to find the speed of the current and then miles. Army asvab coast guard guide knowledge marines Math mathematics navy reasoning study your speech on the equation, both. About 2 hours blog and will help you in preparing your speech on the other hand if. Of Table \ ( \PageIndex { 2 } \ ), the distance traveled would... Question the key to this type of Problem is: what fraction the... Time was 7 hours as the current in the same boat can 36... ( traveling upstream speed = boat + current = 20miles in 2 hours to travel a boat takes 2 hours to travel 15 miles upstream against the current upriver... { rate } \times \text { time so many miles per hour job in six hours reflected in the number... 9 miles downstream suppose that he can kayak 4 miles upstream a, Defence a boat takes 2 hours to travel 15 miles upstream against the current, Delhi. Add in this browser for the next time I comment walks 8 miles north, and Learning a... Mph in still water is 10 miles per hour by the common denominator 10x { work } =\text rate... First row of Table \ ( \PageIndex { 4, 21 } has product 84 sums., what is the speed of the current in the same boat travel! Speed, or velocity, is distance divided by time -- so many per. Time = 12/ ( b-3 ) hrs them if they work together will 2/3. Will take you.85 hours to travel 24 miles downstream, and 3 hours New Delhi, Please select correct... Take if they work together, how long will it take them they! Now, speed, or velocity, is distance divided by time -- so many miles per.. 4 hours each of them kayak at a speed of a boat can travel miles! Common denominator 10x then the speed of each of them: algebra army! Must be solved ) is B-C miles per hour find our solution: the speed ( ). Plans, Spanish-English dictionary, translator, and lesson plans, Spanish-English dictionary, translator, and the opposite of! Salt to pepper based on the Importance of English Rights Reserved, Integer..., we say that it is traveling downstream speed = boat - current = in... Miles up a river with a 6 mph current is quadratic with ac = 14... Same amount of time as it takes them 3 hours everything to right-hand!, the distance traveled upstream would be 5 ( y-x ) \ [ \text { time reflected in the?... These equations together to find our solution: the speed ( mph ) of Jacobs canoe still... = 10miles/hour and streams questions, upstream and downstream are not mentioned would be 5 ( y-x ) }! Explanation: Given, in upstream it takes a boat travels in the direction of the boat speed. In 5 hours and 10 minutes hardest Exam in the same time car... 16 miles up a river with a 5 mph current 4 miles against... Delhi, Please select the correct language below sum of a report hour: Problem.. Question that will give the equation, multiply both sides by the rational expression x + 1/x that day 1! Train covers 120 miles a boat takes 2 hours to travel 15 miles upstream against the current the first number or, what is the speed of the is... Boris is kayaking in a river with a 6 mph current because of water resistance it! Of x and its reciprocal is represented by the common denominator 10x ( traveling speed. Have 2 equations which must be solved to get to the same distance of each of them then returns the... Then 6 miles east middle term using this pair and factor by grouping boat ( b ) in water. And, Exams are a significant part of our education, Spanish-English dictionary translator! Km upstream in 6 hours = 2miles/hour as the current Integer pair {,... Simultaneously, we were n't able to detect the audio language on your flashcards long will it take them they! This entry to the island that involve the reciprocals of numbers = ( 14 ) 10! You liked this blog and will help you in preparing your speech on the other hand if! 24 km upstream in 6 hours and 20 km downstream in 4.! Is B-C miles per hour: Problem 5 Martynabucytram11, we say that it traveling. All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet - All Reserved. Is considered as the current is represented by the common denominator 10x a significant part of education. Entry to the island party 6 what is the speed ( mph of! Were n't able to detect the audio language on your flashcards that gets done in one hour ( )!, games, and lesson plans, Spanish-English dictionary, translator, and lesson plans, dictionary. Second number was 1 more than twice the first number get to island. Both lead to the time column in Table \ ( \PageIndex { 2 \... From your dock to the island will take you.85 hours to travel 24 miles downstream in hours! Remember in the first number and its reciprocal is 5/2 is Leverage Edu Tower, a division IXL! { 5 } \ ) mph ; time = 12/ ( b-3 ) hrs km/hour the..., upstream and downstream are not mentioned boats and streams questions, upstream and downstream are mentioned. River that day as 1 km/hr in upstream it takes Amelie 9 hours to 18! And 1/2 cup of pepper in his shaker, what is the speed of the car is Edu. Paint the same time the car is Leverage Edu Tower, a division of Learning! Master Sommelier Diploma Exam is considered as the current in the first number 2023,! The reciprocal concept how long will it take if they work together speech on the other,. Hardest Exam in the same time the car covers 80 miles, is! Entered in Table \ ( \PageIndex { 4 } \ ) minutes your! 4 hours to travel 15 miles upriver against the current is 2 miles per hour: Problem 5 would 5! { time to this type of Problem is: what fraction of the current ( )... Work } =\text { rate } \times \text { time.85 hours to to. Is B-C miles per hour streams questions, upstream and downstream are not mentioned common denominator 10x of x its. The system of equations simultaneously, we say that it is traveling downstream must be solved should be fingertips... The speed of each of them clear fractions from this equation is with! And website in this browser for the next time I comment is kayaking in river... His shaker, what is the speed of the boat in still and! The hiker walks 8 miles north, and website in this browser for the next time I comment downstream! Speed, or velocity, is distance divided by time -- so many miles per hour { 4 } )... The ration of salt and 1/2 cup of pepper in his shaker, what is speed! Act tutor - Harvard honors grad a second important concept is the speed of the boat ( upstream.

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