Question

A swimming pool can be filled by an inlet pipe in 3 hours. It can be drained by a drainpipe in 6 hours. By mistake, both pipes are opened at the same time. If the pool is empty, in how many hours will it be filled?

Answer 1

`6` hours

Explanation:

Gross input rate: `(1" tank")/(3" hours")`

Gross output rate: `(1 " tank")/(6" hours")`

Net (input) rate: `(1" tank")/(3" hours")-(1" tank")/(6" hours")`

`color(white)("XXXXXXXX")=(1" tank")/(6" hours")color(white)("XXX")` (since `1/3-1/6=1/6`)

`rArr` It will take `6` hours to fill `1` tank

Answer 2

`6` hours to fill.

Explanation:

Let's consider what happens in one hour.

If a pool fills in 3 hours, it means that after 1 hour it is `1/3` full.

If a pool empties in 6 hours, it means that in 1 hour it loses `1/6`

So if it is filling and draining at the same time, after one hour the difference would be:

`1/3-1/6 = 1/6`

The nett result is that the pool fills at a rate of `1/6` per hour.

`1 div 1/6 = 6` hours to fill.