Question

With both taps open, Blake can fill his kitchen sink in 6 minutes. When full, the sink drains in 10 minutes. How long will it take to fill the sink if Blake forgets to put in the stopper?

Answer 1

The time to fill the sink if Blake forgets to put in the stopper would be 15 mins.

Explanation:

Given that,

The kitchen sink can fill in: 6 mins

The sink can drain in: 10 mins

We have to find the time to fill the sink if Blake forgets to put in the stopper. For that,

Lets say, the full tank = 1

Filling rate =
`(x)/(6)`

Drainage rate =
`(x)/(10)`

Hence, the time to fill the tank would be:

`(x)/(6) - (x)/(10) = 1`

`30.(x)/(6) - 30.(x)/(10) = 30.1` (Multiply by LCM)

`5x - 3x = 30`

`2x = 30`

x = 15

Hence, the time to fill the sink if Blake forgets to put in the stopper would be 15 mins.