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?

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Answer 1 · 2016-08-16T19:18:23

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

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

or

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

or

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

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

or

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

or

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

or

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

or

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

or

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

or

$1$ $1$ bathtub gets filled in $4.42$ $4.42$ minutes

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