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Pool and Taps Puzzle - Solution

The Puzzle:

A pool has four faucets.

The first faucet takes two days to fill the pool, the second faucet three days, the third four days and the last one only 6 hours.

How long will it take to fill the pool using all 4 faucets at once?

Our Solution:

First, work out how much of the pool gets filled by each faucet in one hour.

The first faucet takes 48 hours to fill the pool, so in one hour it fills 1/48 of the pool
The second faucet 1/72
The third faucet 1/96
And the fourth faucet fills 1/6 of the pool

We need to add all those fractions together:

1/48 + 1/72 + 1/96 + 1/6 = 6/288 + 4/288 + 3/288 + 48/288 = 61/288

So, in one hour the pool will be 61/288 full

And it will be completely full in 288/61 hours = 4 hours 43 minutes and 17 seconds.

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