Question

A tank can be filled by a pipe in 7 hours. While a drain pipe can empty the tank in 11 hours. If the first 4 hours, the drain was left open while the pipe is filling it. How long will the tank be filled with water?

Answer 1

Let x = time (hours) for second pipe to fill alone
then
3(1/4 + 1/x) = 1
multiplying both sides by 4x:
3(x + 4) = 4x
3x + 12 = 4x
12 hours = x

Answer 2

Another solution:

1st pipe rate = 1/4 job/hr
---
Together rate = 1/3 job/hr
----
2nd pipe rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/4 + 1/x = 1/3
Multiply thru by 12x to get:
3x + 12 = 4x
x = 12 hrs (time required for the 2nd pipe to do the job alone) @stupidinmath