# It takes 7 minutes to fill a bathtub using coldwater faucet alone. It takes 12 minutes using the hot water faucet alone. How long will it take to fill the tub using both?

Aug 16, 2016

By using both the faucets bathtub gets filled in $4.42$ minutes

#### Explanation:

By cold water faucet $7$ minutes to fill $1$ bathtub

or

$1$ minute to fill $\frac{1}{7}$ bathtub
Similarly;
By hot water faucet $12$ minutes to fill $1$ bathtub

or

$1$ minute to fill $\frac{1}{12}$ bathtub

By using both we can write
$1$ minute to fill $\left(\frac{1}{7} + \frac{1}{12}\right)$ bathtub

or

$1$minute to fill $\left(\frac{1}{7} + \frac{1}{12}\right)$ bathtub

or

$1$ minute to fill $\left(\frac{12 + 7}{84}\right)$ bathtub

or

$1$ minute to fill $\left(\frac{19}{84}\right)$ bathtub

or

$\left(\frac{19}{84}\right)$ bathtub gets filled in $1$ minute

or

$1$ bathtub gets filled in $\frac{84}{19}$ minutes

or

$1$ bathtub gets filled in $4.42$ minutes

Therefore by using both the faucets bathtub gets filled in $4.42$ minutes