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 $4.42$ minutes

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

or

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

or

$1$ minute to fill $1/12$ bathtub

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

or

$1$ minute to fill $(1/7+1/12)$ bathtub

or

$1$ minute to fill $((12+7)/84)$ bathtub

or

$1$ minute to fill $((19)/84)$ bathtub

or

$((19)/84)$ bathtub gets filled in $1$ minute

or

$1$ bathtub gets filled in $84/19$ minutes

or

$1$ bathtub gets filled in $4.42$ minutes

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