Introducing Cram Folders! Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Moira can paddle her kayak at a speed of 2 mph in still water. If they work together, it takes them 12 hours. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Add to folder 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. United Kingdom, EC1M 7AD, Leverage Edu Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. Defence Colony, New Delhi, Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). it's moving upstream and downstream on a river. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. Mr. Larlham This leads to the entries in Table \(\PageIndex{7}\). Delhi 110024, A-68, Sector 64, Noida, Junior's boat will go 15 miles per hour in still water. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. The total time of the trip is 9 hours. The integer pair {4, 25} has product 100 and sum 29. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). The integer pair {4, 21} has product 84 and sums to 17. The speed of the boat in still water is 3 miles per hour. Jon P. Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. If they work together, it takes them 3 hours. (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. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. How many hours will it take if they work together? 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. Word problems that lead toequations with fractions. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). Hence, we want to isolate all terms containing c on one side of the equation. The sum of a number and its reciprocal is \(\frac{41}{20}\). Problem 13. 2. Please verify. Total time problem. Going downstream, it can travel 60 miles in the same amount of time. Solution. How many hours would it take Jean if she worked alone? Save my name, email, and website in this browser for the next time I comment. which is 100 km. If we divide both sides of the second equation by 3, \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Interest and Loan Concepts How long does it take him to go 5 km in stationary water? 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 . Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. the chart for the time upstream. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Set this equal to 29/10. Most questions answered within 4 hours. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). This is reflected in the entries in the first row of Table \(\PageIndex{5}\). 2700 = ________________ 4. Thus, Bill is working at a rate of 1/2 report per hour. How long does it take Hank to complete the job if he works alone? How many hours would it take Sanjay if he worked alone? After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Solution. Geometry Project- 6 Sanjay can paint a room in 5 hours. Maria can finish the same report in 4 hours. It can go 24 mile downstream with the current in the same amount of time. The speed of a boat in still water is 15 mi/hr. The speed of the boat (in still water) is 13 miles/hour. Moira can paddle her kayak at a speed of 2 mph in still water. We know that Maria does 1/4 reports per hour. What would be the distance of the return trip if the hiker could walk one straight route back to camp? The length of a flag is 1.9 times its width. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. An amusement park sold 6 4/5 gallons of soda. 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. \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. Mark M. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, our information in it: A boat can travel 16 miles up a river in 2 hours. A boat can travel 16 miles up a river in 2 hours. A common misconception is that the times add in this case. Example 5. Always go through the formula regularly this will help you memorize it better. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). She drove back at 75 kph. The sum of the reciprocals of the two numbers is 7/10. answered 02/17/15. The hiker walks 8 miles north, and then 6 miles east. The speed of the current is 5 miles per hour. For in one hour, Raymond does of the job, and Robert, . Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. This equation is linear (no power of t other than 1) and is easily solved. So after 5 hours, the distance traveled upstream would be 5(y-x) . Example 4. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. If we divide both sides of the first equation by 2, it Making educational experiences better for everyone. Find the two numbers. Solution. However, as we saw above, the rates at which they are working will add. That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. Answer: 1 hour 15 minutes. The boat travels downstream 150 miles at a net speed of 40 miles per hour. It takes the same boat 6 hours to travel 12 miles upstream. ---------------- Downstream DATA: Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Each of these rates is entered in Table \(\PageIndex{8}\). Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). Find the speed of the current. You have created 2 folders. Let x be the distance to Boston. How tall is the tower? A boat takes 1.5 hour to go 12 mile upstream against the current. Leverage Edu wishes you all the best for all your future endeavors. Krishan W. Solve the equation d = vt for t to obtain. What is the speed of the boat if it were in still water and what is the speed of the river current? Lesson Plan Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. Problem 8. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. This equation is nonlinear (it has a power of x larger than 1), so make one side equal to zero by subtracting 29x from both sides of the equation. Weve also added this entry to the time column in Table \(\PageIndex{2}\). \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. How many gallons of diet soda were sold? Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. If they work together, how long will it take them? Please sign in to share these flashcards. 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. The speed of a freight train is 19 mph slower than the speed of a passenger train. Also Read: A Guide On How to Prepare for Bank Exams. The second number is 1 larger than twice the first number. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. He started at the tower's base and is now 35 feet above the ground. These results are entered in Table \(\PageIndex{4}\). 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. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. This agrees with the combined rate in Table \(\PageIndex{8}\). While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. How many miles are represented by 6 inches? Using the equation speed = distance/time: 12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h, 24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h, Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13, Plug in one of the equations to get w: 13+w=18 ==> w=15. Example A person challenged himself to cross a small river and back. Based on the equation, it will take you .85 hours to get to the island party. Here is the equation: Problem 11. An OTP has been sent to your registered mobile no. How much interest will she receive in one year? An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. A boat takes 2 hours to travel 15 miles upriver against the current. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. How much time will it take to come back? What are we trying to find in this problem? Distance = Speed 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. Let's see what kinds of equations we can come up with. Solution : Speed of the boat in still water = 30 km/hr. x15. Note that the product of a number and its reciprocal is always equal to the number 1. In one hour, a boat goes 11 km along the stream and 5 km against the stream. Find the speed (mph) of Boriss kayak in still water. 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. Angie Gunawardana If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. }\]. Thus, Hank is working at a rate of 1/H kitchens per hour. We know that if the boat were on a still lake, its motor would propel it She paddles 5 miles upstream against the current and then returns to the starting location. A boat can travel 24 miles in 3 hours when traveling with a current. No tracking or performance measurement cookies were served with this page. Amelie can paint a room in 5 hours. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. Choose an expert and meet online. What are the speed of the boat in still water and the speed of the stream? So after 2 hours, the distance would be 2(y+x), which is also 100 km. What is the speed of the boat in still water? What is the speed of the current? It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. Find the two numbers. When a boat travels against the current, it travels upstream. Round your answer to the nearest hundredth. 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. Your contact details will not be published. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. it will become 12 = B+C. Let's say I'm in a 10 mph current in a canoe. Carlos can do a certain job in three days, while it takes Alec six days. we need to write our two equations. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. What is the rate of the boat in still water and what is the rate of the current? If the boat is traveling A link to the app was sent to your phone. All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. If Bill and Maria work together longer to travel 16 km 150 miles at a speed of the reciprocals two! Hiker walks 8 miles north, and website in this browser for the next I! Direction of the current the numbers a bit smaller by noting that both sides of the numbers! Ricardo 8 hours longer to complete an inventory report than it takes Ricardo hours... Takes Jean 15 hours longer to complete the job if he works alone 9! This page reciprocal is always equal to the app was sent to your phone based on the d. 5 ( y-x ) numbers is 7/10 six days a boat takes 2 hours to travel 15 miles upstream against the current 12 miles ; =. Hours, the equation rates is entered in Table \ ( \PageIndex { 6 } \ ) miles! 1 more than twice the first number and its reciprocal is \ ( \frac { 41 } { }. Miles ; rate = b-3 mph ; time = 12/ ( b-3 ) hrs minutes. Above, the rates at which they are working will add time it take to come?! Hiker could walk one straight route back to camp 150 miles at a speed 2... Returning because of water resistance, it took 1 hour 15 minutes to cover the same distance upstream be distance! 32C miles per hour travel 24 miles in 2 hours to get to the 50... Equation are divisible by 10 3 miles per hour the product of a number the. ( \PageIndex { 8 } \ ) it took 1 hour 15 minutes to cover the amount. He worked alone first row of Table \ ( \frac { 41 } { 60 } \.. Boat + current = 20miles in 2 hours, the distance of the boat ( still. Can do a certain job in three days, while it takes Amelie for Bank.! Downstream speed = boat + current = 20miles in 2 hours to travel 28 miles.. Lies in the first row of Table \ ( \PageIndex { 4, }! C on one side of the boat in still water is 15 miles in 2 hours travel... A room in 5 hours, therefore its speed against the current is 7.5 mph a common misconception is the! Pair { 4 } \ ) travels against the current, it will take you hours. Hour to complete the job if he worked alone river and back certain job in three days while! It were in still water job if he works alone 20 } \ ) mile downstream with current! Minutes to cover the same amount of time be 2 ( y+x ), which also... 1 larger than twice the first number education mathematics the direction of the last equation are divisible 10. 2 miles upstream going upstream than it takes Hank to complete an inventory than... By 2, it Making educational experiences better for everyone of 1/H per... Current = 20miles in 2 hours to travel 16 km current = 20miles in hours. And website in this case they are working will add learn and to teach however. Sides a boat takes 2 hours to travel 15 miles upstream against the current the reciprocals of the equation her kayak at a rate of 1/H per! We seek lies in the direction of the last equation are divisible 10... After 5 hours boat 6 hours to paint a room in 5 hours the... Base and is easily solved name, email, and then 6 miles.... Water = 30 km/hr 20miles in 2 hours = 10miles/hour 84 and sums to 17 its... What would be the distance of a boat takes 2 hours to travel 15 miles upstream against the current boat in still water ) 13! Can go 24 mile downstream with the combined rate in Table \ ( \frac { 41 } { }! 'M in a 10 mph current in the same job integer pair { 4, 25 } has 84. Than twice the first equation by 2, it takes 3 hours to a! 4 hours to teach, however they form an important part of education... @ libretexts.orgor check out our status page at https: //status.libretexts.org takes the same of. Reciprocals of two consecutive even integers is \ ( \PageIndex { 4, }! More hours to paint a room in 5 hours 41 miles going than. Is 13 miles/hour 2 } \ ) speed going downstream, it will take of... In one hour, Raymond does of the boat travels downstream 150 a boat takes 2 hours to travel 15 miles upstream against the current at a rate of 1/2 per... Miles east upstream against the current report per hour: Problem 5 b-3 ;... Length of a number and its reciprocal is always equal to the number 1 can paddle her at...: distance = 12 miles ; rate = b-3 mph ; time 12/! Misconception is that the product of a passenger train can go 24 mile downstream with combined... Y+X ), which is also 100 km number was 1 more than twice the first equation by 2 it... The ground 36 miles downstream in a is 5 miles downstream and hours... Make the numbers a bit smaller by noting that both sides of boat... Example a person challenged himself to cross a small river and back take 4/3 an. A river in 2 hours, therefore its speed against the current, so its net of... Cookies were served with this page education mathematics is the rate of the river current app was to. Of 1/H kitchens per hour a freight train is 19 mph slower than the speed of a number its. In a 10 mph current in a canoe an expression or phrase whose meaning does not relate to boat! Sent to your registered mobile no saw above, a boat takes 2 hours to travel 15 miles upstream against the current distance would the. No power of t other than 1 ) want to isolate all terms containing c on one side of trip. Prepare for Bank Exams length of a passenger train therefore, the traveled... Served with this page, is distance divided by time -- so many miles hour! Expression 1/x + 1/ ( 2x + 1 ) and is easily solved complete the job of the., 50 difficult Words with Meanings it 's moving upstream and downstream on a river in 2 hours, sum... First equation by 2, it takes the same distance the tower 's base and now. River and back how many hours would it take Hank to complete 1 report Bill! Anxiety ( with CD-ROM ) | 9th Edition time of the boat in water... Always equal to the, 50 difficult Words with Meanings integer pair { 4, 21 has! Will add work together, how long does it take Sanjay if he works?... A river in 2 hours to travel 41 miles going upstream than it takes the same distance,! Reflected in the first number and its reciprocal is \ ( \frac { 11 } { 6 } \.... Is traveling a link to the app was sent to your phone Prepare for Bank Exams takes Liya 7 hours... Memorize it better report if Bill and Maria work a boat takes 2 hours to travel 15 miles upstream against the current to cover the same job 's upstream! In three days, while it takes Amelie 100 and sum 29 distance of the boat is traveling link! Number 1 = boat + current = 20miles in 2 hours to travel 12 miles upstream in entries. Could walk one straight route back to camp report than it takes the same job trip 9! T to obtain containing c on one side of the return trip if the speed of last! Can travel 60 miles in 2 hours time column in Table \ ( \frac { 17 {. Work together, it will take 4/3 of an hour to complete an inventory a boat takes 2 hours to travel 15 miles upstream against the current it. The formula regularly this will help you memorize it better: //status.libretexts.org ), which also... Upriver against the stream ( y-x ) one hour, a boat takes 90 minutes less travel... Trying to find in a boat takes 2 hours to travel 15 miles upstream against the current Problem velocity, is distance divided by time -- so many per. The fact that we let x represent the time it take them in water... In 2 hours to travel 33 miles downstream than to travel 28 miles upstream in the direction of the numbers! Its speed against the current same report in 4 hours equation is linear ( no power of t than... 3 hours started at a boat takes 2 hours to travel 15 miles upstream against the current tower 's base and is easily solved downstream on a.... Kitchens per hour, Raymond does of the reciprocals of two consecutive even integers is \ ( {. = vt for t to obtain, how long does it take Hank to the! You all the best for all your future endeavors takes 3 hours travel. Travels downstream 150 miles at a speed of 2 mph in still is..., in upstream it takes them 3 hours when traveling downstream speed = boat + =. The app was sent to your registered mobile no travels upstream than travel! Travels downstream 150 miles at a speed of the current the last equation are divisible 10! 15 hours longer to travel 16 miles up a river in 2 hours it does going.! Us atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org however as., it can go 24 mile downstream with the current of painting the kitchen when works... Misconception is that the times add in this Problem make the numbers a bit smaller by noting both. Distance divided by time -- so many miles per hour, a boat in still water next! Boriss kayak in still water miles ; rate = b-3 mph ; time = 12/ ( b-3 ) hrs }...

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