Question

Using faucet P, you can fill a sink in 10 minutes. Faucet Q takes only 8 minutes to fill the same sink. How long will it take to fill the sink using both faucets together?A. 4 4/9 minB. 4 2/9 minC. 8 2/9 minD. 8 4/9 min

Answer 1

Let V be the volume of the sink; therefore, according to the question,

$\begin{gathered} v_p=\frac{V}{10} \\ and \\ v_q=\frac{V}{8} \end{gathered}$

Where v_p and v_q stand for the speed at which faucet P and faucet Q fill the sink, respectively.

Therefore,

$\begin{gathered} (v_p+v_q)t=V \\ \Rightarrow t=\frac{V}{(v_p+v_q)} \end{gathered}$

Thus,

$\Rightarrow t=\frac{V}{\frac{V}{10}+\frac{V}{8}}=\frac{V}{\frac{9V}{40}}=\frac{40}{9}=4+\frac{4}{9}$

Therefore, the answer is option A. 4 4/9 minutes.