Two pumps working together drain a pool in $6$ $6$ hours. If older pump itself drains out the pool in $14$ $14$ hours, how much time will newer pump take to drain the pool?

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Answer 1 · 2017-02-22T05:59:02

Newer pump can drain out the pool in $10 \frac{1}{2}$ $10 1/2$ hours.

As two pumps working together drain the pool in $6$ $6$ hours,

in one hour, they drain $\frac{1}{6}$ $1/6$ of the pool.

As older pump itself drains the pool in $14$ $14$ hours

as such in one hour, older pump can drain $\frac{1}{14}$ $1/14$ of the pool.

As in one hour, two pumps together drain out $\frac{1}{6}$ $1/6$ of the pool and older pump drains out $\frac{1}{14}$ $1/14$ of the pool

newer pump on its own must be draining

$\frac{1}{6} - \frac{1}{14} = \frac{7 - 3}{42} = \frac{4}{42} = \frac{2}{21}$ $1/6-1/14=(7-3)/42=4/42=2/21$ of the pool

Hence, newer pump can drain out the pool in $\frac{21}{2} = 10 \frac{1}{2}$ $21/2=10 1/2$ hours.

Two pumps working together drain a pool in 66 hours. If older pump itself drains out the pool in 1414 hours, how much time will newer pump take to drain the pool?