A tank can be fully filled with water using a pipe that fills 20 liters in a minute. A bigger pipe that can fill 25 liters in a minute .. will take one minute less to fill the same tank. How many...
A tank can be fully filled with water using a pipe that fills 20 liters in a minute. A bigger pipe that can fill 25 liters in a minute ..
will take one minute less to fill the same tank. How many minutes does the smaller pipe take to fill the tank?
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let the volume of the tank be V ( in litres)
The rate of filling the tank with a smaller pipe is 20 L / m
Then, the time will be taker to fill the tank is T1 = V/20 .......(1)
Now with the bigger pipe, the rate is 25 L / m
Then the time will be taken to fill the tank is T2 = V/25
But the time taken is one minute less than the time required to fill with smaller pipe.
==> T2 = T1 - 1
==> T1 -1 = v/25
==> T1 = v/25 + 1............(2)
Now from (1) and (2) we conclude that:
v/25 + 1 = v/ 20
==> (v+25) / 25 = v/20
==> (v+25) /5 = v/ 4
We will multiply by 20.
==> 4(v+25) = 5v
==> 4v + 100 = 5v
==> V = 100 litre
==> T1 = v/20 = 100/20 = 5 minutes.
Then, the time required to fill the tank with the smaller pipe is 5 minutes.
Related Questions
- Two pipes fill a storage tank in 9 hours. The smaller pipe takes 3 times as long to fill the...
- 1 Educator Answer
- How long does it take to empty the tank using 2 of the smaller pipes, in the following case?If...
- 1 Educator Answer
- 2 taps A and B can fill a bucket in 12 and 18 minutes resp. How long will it take both the taps...
- 2 Educator Answers
- If both are used together, how long will it take to fill the empty tanker of an oil tanker that...
- 2 Educator Answers
- Water flows through a cylinder pipe of radius 0.74 cm. It fills a 12 litre bucket in 4 minutes....
- 1 Educator Answer
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
Let the time taken to fill the tank with the smaller pipe be T. This pipe fills at the rate of 20 liters/ minute.
So the capacity of the tank is 20T.
The bigger pipe fills at 25 liters/ minute and takes 1 minute less.
So we have 20T / 25 = T - 1
=> 20T = 25T - 25
=> 5T = 25
=> T = 5
Therefore the smaller pipe takes 5 minutes to fill the tank.
Let V be the volume of the tank in litres.
Then at the rate of 20 litre per minute the smaller pipe takes V/20 minutes.
Then the bigger pipe takes V/20-1 minutes by data which should also be equal to V/ 25 minutes.
Therefore V/20 -1 = V/25. Multiplying by 20*25 we get:
25V - 20*25 = 20 V.
So 25V- 20 V = 20*25.
5V = 20* 25.
V = 20*25/ 5 = 100 litre.
So the smaller pipe takes 100/20 = 5 minutes.
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers