Draining Reservoir

A large fresh water reservoir has two types of drainage system: small pipes and large pipes.

6 large pipes, on their own, can drain the reservoir in 12 hours.

3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.

How long will 5 small pipes, on their own, take to drain the reservoir?

Find here the exact time required! 

Time To Drain The Reservoir

Here is the question! 

Let T be the capacity of the tank. Let L be the large pipe and S be the small pipe.

T/6L = 12

L = T/72

T/(3L + 9S) = 8

Putting L = T/72,

S = T/108

Hence T/5S = 108/5 gives S = 21.6 hours.

To conclude, small pipes require 21.6 hours i.e. 21 hours and 36 minutes to drain the reservoir.