A tank is three-fourth full. Pipe A can fill the tank in 12 minutes. Pipe B can empty it in 8 minutes. If both pipes are open, how long will it take to empty the tank?
Answers
Answer:given below Step-by-step explanation:
let t = time to empty the tank with both pipes open
Let a full tank = 1, then 3/4 of a tank = .75
:
t%2F8 - t%2F12 = .75
multiply by 24, cancel the denominators
3t - 2t = 24(.75)
t = 18 minutes to empty the tank
Time taken to empty the tank is 18 minutes.
Given:
Quantity of tank full = 3/4
Time taken by tank A to fill = 12 mins
Time taken by tank B to fill = 8 mins
To Find:
If both pipes are open, how long will it take to empty the tank?
Solution:
Let the time taken to empty the tank be = t
The tank when full = 1
Therefore, if 3/4 is open =
= 1 - 3/4
= 1/4
= 0.75
According to the question, considering both pipes -
= t/8 - t/12 = 0.75
= 12t - 8t/96 = 0.75
4t = 0.75 × 96
4t = 72
t = 72/4
t = 18
Answer: Time taken to empty the tank is 18 minutes.
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