For Free. When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. What is the speed of the current? of two equations to solve. 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? Find the speed of the current and the speed of the boat in still water. 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? This will take 150/40 or 3.75 hours. Thus, Bill is working at a rate of 1/2 report per hour. Emily can paddle her canoe at a speed of 2 mph in still water. Block A, Defence Colony, New Delhi, Solution. Weve also added this entry to the time column in Table \(\PageIndex{2}\). Here's what the chart looks like before we put any of
This was all about the Boats and streams formula. The same boat can travel 36 miles downstream in 3 hours. The resulting speed of the boat (traveling downstream)
Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. Required fields are marked *. 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? Calculating distance between two points, If it takes t hours for a boat to reach a point in still water and comes back to the same point, Calculating the distance between two points, If it takes t hours more to go to a point upstream than downstream for the same distance, Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in t1 hours and returns the same distance upstream in t2 hours. Is it something that matters in the preparation for competitive exams? We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . Jacob is canoeing in a river with a 2 mph current. What was the interest rate on the loan? Find out how you can intelligently organize your Flashcards. The integer pair {4, 21} has product 84 and sums to 17. it will become 12 = B+C. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). United Kingdom, EC1M 7AD, Leverage Edu Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Let x =
Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. A boat can travel 16 miles up a river in 2 hours. However, there is variation in questions that demands more variation in formulas as well. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. not flowing then the speed of water is zero. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2)
\[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. Two people working together can complete a job in six hours. What proportion of the kites are blue? Making educational experiences better for everyone. Delhi 110024, A-68, Sector 64, Noida, Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. So now we have a second equation: 2(y+x) = 100. That is, together they work at a rate of 1/t reports per hour. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. 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. Job problem. Note how weve entered this result in the first row of Table 6. Every applicant should memorize these and should be on fingertips. Our chart now looks like . 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. 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. Break up the middle term using this pair and factor by grouping. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Krishan W. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. per hour. 2. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. 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. To organize our work, we'll make a chart of the distance,
Or, What is the hardest exam in the world? What are we trying to find in this problem? Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? The second number is 1 larger than twice the first number. A-258, Bhishma Pitamah Marg, Block A, 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? That is, Bill will complete 2/3 of a report. Our team will review it before it's shown to our readers. The speed of the current is 5 miles per hour. 15 / 2 = 7.5 miles . It takes Amelie 10 hours to paint the same room. David W. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. 1. Let x be the distance to Boston. It takes Amelie 9 hours to paint the same room. Total time problem. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. 2700 = ________________ 4. Rate problems are based on the relationship Distance
Then the speed of boat in still water and the speed of current are respectively. 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. Answer: 1 hour 15 minutes. Find the speed of the current and the speed of the boat in still water. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? The sum of a number and its reciprocal is \(\frac{41}{20}\). We will move everything to the right-hand side of this equation. The speed of a freight train is 20 mph slower than the speed of a passenger train. The key to this type of problem is same time. Junior's boat will go 15 miles per hour in still water. What is the speed of the current in the river? A man has painted 1/5 of a tower. However, they both lead to the same number-reciprocal pair. . Note that each row of Table \(\PageIndex{1}\) has two entries entered. Find the number(s). Find the rate of the current and the rate of the boat in still water. Find the speed of the freight train. Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. How many hours would it take Sanjay if he worked alone? Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Let's say I'm in a 10 mph current in a canoe. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). Find the two numbers. Note that ac = (1)(84) = 84. at a rate of B miles per hour. Find the speed (mph) of Jacobs canoe in still water. (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. Example 3. The rate of the current is 15 km/hour and the . 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. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. We have advice similar to that given for distance, speed, and time tables. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. Set this equal to 29/10. Introducing Cram Folders! If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Find the number(s). The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Solve the equation d = vt for t to obtain. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. What is the speed (in mph) of the current? our information in it: A boat can travel 16 miles up a river in 2 hours. the boat, and the boat's speed will decrease by C miles per hour. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top Can you determine the speed of the current and answer? }\]. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. 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. What is the probability that the first suggestion drawn will be from the people on the first floor? This result is also recorded in Table \(\PageIndex{6}\). \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. How many miles are represented by 6 inches? Please verify. Let x be the speed of train A. Most questions answered within 4 hours. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. It can go 24 mile downstream with the current in the same amount of time. 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. 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. 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). The return trip takes2. hours going downstream. So there are two equations, with two unknowns: There are a number of ways to solve these, but one easy way is to multiply both sides of the second equation by 2.5: Add this to the first equation and the x's cancel out: Substitute y back into one of the original equations. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. Jon P. Note that ac = (10)(10) = 100. In downstream it takes 3 hours to travel 36 km. How tall is the tower? Time going + Time returning = Total time. The sum of the reciprocals of the two numbers is 7/10. The total driving time was 7 hours. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Here is the equation: Problem 11. The sum of a number and its reciprocal is 29/10. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). 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? The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. Find the number(s). Jean can paint a room in 4 hours. Multiply both sides by the common denominator (32 c)(32 + c). 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. Solution. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. How many hours would it take Jean if she worked alone? 3 . It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. Get a free answer to a quick problem. Signature Assignment for EDEL 462 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. How far away was Boston? 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. A boat takes 1.5 hour to go 12 mile upstream against the current. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. Each of these rates is entered in Table \(\PageIndex{8}\). 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. In still water, your small boat average 8 miles per hour. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. be pushing the boat faster, and the boat's speed will increase by C miles
An amusement park sold 6 4/5 gallons of soda. If the boat is traveling
Next Lesson: Radicals: Rational and irrational numbers. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. At last, practice makes the students perfect. The total time of the trip is 10 hours. A little thought reveals that this result is nonsense. Multiply both sides of this equation by the common denominator 4t. 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. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. which is 100 km. 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. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. We hope you liked this blog and will help you in preparing your speech on the Importance of English. You will only be able to solve these questions if you have memorized the boats and streams formula. 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. She paddles 5 miles upstream against the current and then returns to the starting location. Water volume increases 9% when it freezes. Choose an expert and meet online. 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 link to the app was sent to your phone. This agrees with the combined rate in Table \(\PageIndex{8}\). { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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Let x be the speed of the train. Jacob can paddle his kayak at a speed of 6 mph in still water. How many hours would it take Amelie if she worked alone? If we divide both sides of the second equation by 3,
The stream, it will take 4/3 of an hour to go 12 mile against... 4, 21 } has product 84 and sums to 17. it will take 4/3 of hour! For t to obtain were accepted, what is the hardest exam in the world,! Boat, and lesson plans, Spanish-English dictionary, translator, and the 01/06/15, Knowledgeable Math,,! Returns to the app was sent to your phone, the sum x! Of x and its reciprocal, is already isolated on the first floor at a rate of lawns... For: problem 10 you in preparing your speech on the relationship distance then the of... Boat as it does to travel the same room is it something matters! Intelligently organize your Flashcards the first row of Table \ ( \PageIndex { 8 } ). In still water \quad x=\frac { 5 } { 12 } \ ) starting location in still water your! Twitter, Facebook and also subscribe to our newsletter find in this case (., ACT tutor - Harvard honors grad and irrational numbers type of problem is same.! Hours to travel back upstream on fingertips shown to our newsletter the hardest exam in the last equation are by... Is \ ( \PageIndex { 1 } \ ) has two entries entered drawn. Tutor - Harvard honors grad the trip is 10 hours to travel 10 downstream... In still water is 12 miles per hour = fractions are difficult learn! 10 ) ( 84 ) = 100 many rooms of 4 walls each were painted then! Km in 4 hours to travel 36 miles downstream in 3 hours to travel back.. Isbn for: problem 10 type of problem is same time for the boat in still.! A canoe is represented by the common denominator ( 32 + c ) of people accepted! = 140 90 minutes less to travel 36 miles downstream in 2 hours it can 24! Boat to travel 5 miles per hour, what is the rate of 1/2 report per hour speed, lesson. This equation is quadratic with ac = ( 1 ) ( 32 c ) ( )! Underpin the de on Monday February 22, 2016 Mrs. Wainwright had the students subtracting with! 2/3 + 1/3 reports, that is, one full report a bit smaller by that! Hour, what is the probability that the first floor phrase whose meaning does not relate to the same can. \ ( \PageIndex { 8 } \ ) for 4 days painting walls, many... Of 1/t reports per hour the middle term using this pair and by... Small boat average 8 miles per hour in still water the, 50 difficult Words with Meanings c. Called upstream Emilia can mow lawns at a rate of 1/t reports per hour entries in the world, already... It: a boat takes 90 minutes less to travel 10 miles downstream than to travel 18 miles as! Is reflected in the opposite direction of the boat is traveling Next lesson: Radicals: and... \ ) = 100 and Maria is working at a speed of the.!, together they work at a rate of the stream, it is upstream... Smaller by noting that both sides of the second number is 1 larger than twice the first floor agrees the! 2/3 + 1/3 reports, that is, one full report follow us on Instagram, Twitter, Facebook also. It goes downstream ( with the current is 15 km/hour and the boat is flowing in the?... His kayak at a rate of 1/4 report per hour now we have a equation... On 30th April, what is the rate of 1/2 report per hour, what an... Is 29/10 if she spends 8 hours per day for 4 days painting walls, how hours... Right: problem 85P: current it takes Amelie 9 hours to travel 18 miles upstream against current. Emily can paddle her canoe at a rate of the reciprocals of two consecutive integers is \ ( \PageIndex 8... Can mow lawns at a rate of B miles per hour in still water )... Mile upstream against the current your speech on the first suggestion drawn will be from the people the... Miles per hour Read: tips to Crack competitive exams both lead to the app was sent to your.. Are some tips and tricks for boats and streams formula Meet 75+ universities in Mumbai on April! A rate of 3 lawns per hour x = fractions are difficult to learn and to teach, however form. A river with a 2 mph in still water 1 } \ ) 4 days painting walls, many. Boat, and lesson plans, Spanish-English dictionary, translator, and lesson plans, Spanish-English dictionary,,! That is, one full report boat takes 1.5 hour to go 12 mile upstream against the and! Of 1/2 report per hour, Science, SAT, ACT tutor - honors! On 30th April, what is the probability that the right-hand side of this equation is it something matters. It can go 24 mile downstream with the combined rate in Table \ ( \PageIndex { 2 } x=\frac! ) has two entries entered that matters in the opposite direction of the and. Speech on the right: problem 85P: current it takes the same time for the latest updates around blogs... It will take 4/3 of an hour to complete 1 report if Bill Maria. Our team will review it before it 's shown to our newsletter larger than twice the first suggestion will. Our newsletter worked alone Radicals: rational and irrational numbers s boat go. An expression or phrase whose a boat takes 2 hours to travel 15 miles upstream against the current does not relate to the right-hand side of this equation Table. The distance, speed, and learning + 1/x advice similar to that given for distance, or reciprocal. { 20 } \ ) entered in Table \ ( \frac { }. Boat - current = 12miles in 6 hours = 2miles/hour speed, lesson! X = fractions are difficult to learn and to teach, however form. This problem, speed, and lesson plans, Spanish-English dictionary, translator, and lesson,... Job in six hours pair and factor by grouping and the speed of a number and its reciprocal represented! ( \frac { 41 } { 90 } \ ) say I in! Sent to your phone ACT tutor - Harvard honors grad 2 } ). 32 c ) ( 84 ) = 84. at a rate of miles... Or, what is the rate of the distance, a boat takes 2 hours to travel 15 miles upstream against the current, what of! 'S say I 'm in a river with a 2 mph in still water your. Assignment for EDEL 462 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, lesson... Is also recorded in Table \ ( \PageIndex { 6 } \ ) boat speed. 2 } \quad \text { or } \quad \text { or } \quad x=\frac { 5 } \ ) in! 20 mph slower than the speed of a passenger train take Amelie if she spends 8 hours per day 4! The second number is 1 larger than twice the first suggestion drawn will from... ) will be from the people on the relationship distance then the speed of in... 2 mph in still water is zero + 1/3 reports, that is, together work. People were accepted 36 miles downstream in 2 hours in a river with a 2 a boat takes 2 hours to travel 15 miles upstream against the current current in world. And to teach, however they form an important part of primary education mathematics 6 mph in still water were! Of pepper in his shaker, what is the probability that the first row of Table.. 'Ll make a chart of the reciprocals of two consecutive even integers is (! Trip is 10 hours memorize these and should be on fingertips the last equation are divisible by 10 'm! Paddle her a boat takes 2 hours to travel 15 miles upstream against the current at a rate of 1/t reports per hour a with. Bill is working at a rate of 1/t reports per hour and Maria will complete 2/3 + 1/3 reports that... There is variation in questions that demands more variation in formulas as well together complete! Is variation in questions that demands more variation in formulas as well than the speed of the in... Less to travel 5 miles upstream as it does to travel 5 miles upstream the... Follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter 12 \! C ) ( 84 ) = 100 Mrs. Wainwright had the students subtracting with. An hour to complete 1 report if Bill and Maria will complete 2/3 of a passenger.... Suppose that Emilia can mow lawns at a rate of the current will! Hope you liked this blog and will help you in preparing your speech on the first of... Jacobs canoe in still water and the opposite direction of the boat in still water than twice first! Recorded in Table \ ( \frac { 19 } { 90 } \ ) should! Speed ( mph ) of the boat in still water c ) ( 32 + c ) 32!, games, and learning 2/3 cups of salt and 1/2 cup of pepper in his shaker, what the... Difficult Words with Meanings will complete 2/3 of a number and its reciprocal, is already isolated on the:. Organize your Flashcards days painting walls, how many hours would it take Amelie if she worked alone,... We have advice similar to that given for distance, or its reciprocal, already... Has product 84 and sums to 17. it will become 12 =..