Question

It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and hot water faucets take 3 minutes to fill the tub. How long will it take the cold water faucet to fill the tub by itself

Answer 1

If it takes the cold water faucet x minutes to fill 1 tub, then its flow rate is (1 tub)/(x min).

The hot water faucet takes 4 times as long, so its flow rate is (1 tub)/(4x min).

Together, the total flow rate is (1 tub)/(3 min), so we have

$\dfrac1x+\dfrac1{4x}=\dfrac13$

$\implies\dfrac5{4x}=\dfrac13$

$\implies15=4x$

$\implies x=\dfrac{15}4\,\text{min}=3\,\text{min}\,45\,\text{sec}$