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=(V)/(10) \\ and \\ v_q=(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=(V)/((v_p+v_q)) \end{gathered}`

Thus,

`\Rightarrow t=(V)/((V)/(10)+(V)/(8))=(V)/((9V)/(40))=(40)/(9)=4+(4)/(9)`

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