Question

A faucet can fill a sink in 5 minutes. It takes twice as long for the drain the empty a sink. How long will it take to fill the sink if the drain is open and the faucet is on?

Answer 1

Answer: It will take 10 hours to fill the sink if the drain is open and the faucet is on.

Step-by-step explanation:

Since we have given that

Number of minutes that a faucet can fill a sink = 5 minutes

Number of minutes that a faucet can drain the empty a sink = $2\times 5=10\ minutes$

Let the number of minutes that it will take to fill the sink if the drain is open and the faucet is on be 'x'.

According to question, using "Time and Work", we get that

$\dfrac{1}{5}-\dfrac{1}{10}=\dfrac{1}{x}\\\\\dfrac{2-1}{10}=\dfrac{1}{x}\\\\\dfrac{1}{10}=\dfrac{1}{x}\\\\x=10$

Hence, it will take 10 hours to fill the sink if the drain is open and the faucet is on.