BrainBashers : Puzzles and Brain Teasers

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.

6 small pipes, on their own, can drain the reservoir in 18 hours.

How long will 6 large pipes and 6 small pipes take to drain the reservoir?

7 hours and 12 minutes.

The exact size of the pipes and reservoir does not matter. If we label the large pipes L, the small pipes S and if the reservoir has a total of T litres, then:

   T ÷ 6L = 12 which means L = T ÷ 72

and

   T ÷ 6S = 18 which means S = T ÷ 108

we want T ÷ (6L + 6S)

   = T ÷ ((6 x T ÷ 72) + (6 * T ÷ 108))

   = T ÷ ((648 x T + 432 x T) ÷ 7776)

   = T ÷ ((1080 x T) ÷ 7776)

   = 7776 x T ÷ (1080 x T)

   = 7776 ÷ 1080

   = 7.2 hours

   = 7 hours and 12 minutes. QED.