SOLUTION: A pump is filling a tank with water at a constant rate while water in the tank is also drained by 3 identical pipes. Starting from a full tank of water with water being pumped

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Question 1137878: A pump is filling a tank with water at a constant rate while water in the tank is also drained by 3 identical pipes.
Starting from a full tank of water with water being pumped into it, the tank can be completely drained by the 3 identical pipes in 35 minutes.
If an additional identical pipe is installed to drain the tank, a full tank of water can be completely drained in 20 minutes when water is pumped into it.
How many minutes will it take for the pump to fill an empty tank with water to its brim without any pipe to drain water from the tank?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A pump is filling a tank with water at a constant rate while water in the tank is also drained by 3 identical pipes.
Starting from a full tank of water with water being pumped into it, the tank can be completely drained by the 3 identical pipes in 35 minutes.
If an additional identical pipe is installed to drain the tank, a full tank of water can be completely drained in 20 minutes when water is pumped into it.
How many minutes will it take for the pump to fill an empty tank with water to its brim without any pipe to drain water from the tank?
:
let f = time to fill the tank with no draining pipes
let p = time for 1 pipe to drain a full tank
let the completed job = 1; an empty tank
:
Three pipe equation
35%2Ff - 335%2Fp = 1
Four pipe equation
20%2Ff - 420%2Fp = 1
:
35%2Ff - 105%2Fp = 1
20%2Ff - 80%2Fp = 1
:
multiply the 2nd equation by 7 and the 1st equation by 4
140%2Ff - 560%2Fp = 7
140%2Ff - 420%2Fp = 4
---------------------------------Subtraction eliminates f, find p
0 - 140%2Fp = 3
3p = -140
p = -140/3
p = -46.67 minutes for a single pipe to drain a full tank
find f
20%2Ff - 80%2F-46.67 = 1
multiply by -46.67f
-46.67(20) + 80f = -46.67f
Multiply by -1
46.67(20) - 80f = -46.47
933.33 = -46.67f + 80f
933.33 = 33.333f
f = 933.33/33.333
f = 28 minutes for tank to be filled without drains
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