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

Answer:

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 = $\frac{1}{time}$ = $\frac{1}{t}$

Rate at which cold water faucet fills the sink = $\frac{1}{time}$ = $\frac{1}{4}$

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

$\frac{1}{t}$ + $\frac{1}{4}$ = $\frac{1}{3}$

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.