Question

A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in 4 minutes. If both faucets are open, the sink is filled in 3 minutes. How long does it take to fill the sink with just the hot water faucet open?

Answer 1

Given:

Cold water faucet fills the sink in 4 minutes.

Both faucets fills the sink in 3 minutes.

Let us assume that "t" be the time it takes hot water faucet in order to fill the sink.

Therefore;

Rate for hot water faucet fills the sink =
`(1)/(time)` =
`(1)/(t)`

Rate at which cold water faucet fills the sink =
`(1)/(time)` =
`(1)/(4)`

When both faucets are used , the rate at which they fill the sink is given as :

`(1)/(t)` +
`(1)/(4)` =
`(1)/(3)`

On solving the above equation, we get :

`4t = 3t +12`

∴
`t = 12\ minutes`

Therefore, it takes 12 minutes for the hot water faucet to fill the sink.