Question

A​ cold-water faucet can fill a sink in 1212 ​min, and a​ hot-water faucet can fill it in 1515 min. The drain can empty the sink in 2525 min. If both faucets are on and the drain is​ open, how long will it take to fill the​ sink?

Answer 1

9.1 minutes.

Explanation:

Let t represent time taken to fill the tank.

We have been given that a cold water faucet can fill a sink in 12 ​min, so the part of sink filed in 1 minute would be
`(1)/(12)`.

The hot-water faucet can fill it in 15 min, so the part of sink filed in 1 minute would be
`(1)/(15)`.

The drain can empty the sink in 25 min, so the part of drain emptied in 1 minute would be
`(1)/(25)`.

The part of 1 full tank filled in t minutes, when both faucets are on and the drain is​ open would be:

`((1)/(12)+(1)/(15)-(1)/(25))t=1`

Make a common denominator:

`((1*25)/(12*25)+(1*20)/(15*20)-(1*12)/(25*12))t=1`

`((25)/(300)+(20)/(300)-(12)/(300))t=1`

`((25+20-12)/(300))t=1`

`(33)/(300)t=1`

`(11)/(100)t=1`

`(100)/(11)* (11)/(100)t=(100)/(11)*1`

`t=(100)/(11)`

`t=9.0909`

`t\approx 9.1`

Therefore, it will take 9.1 minutes to fill the sink.