# Math

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Two hoses are connected to a swimming pool. Working together, they can fill the pool in 4 hr. The larger hose, working alone, can fill the pool in 6 hr less time than the smaller one. How long would it take the smaller one, woking alone, to fill the pool?

• Math -

The large one can fill in x hours,
then the small one in (x+6) hours.
During each hour, working together, the two hoses can fill 1/x+1/(x+6) of the pool, or (2x+6)/(x(x+6)).

Since using both hoses, it fills the pool in 4 hours, each hour fills 1/4 of the pool, therefore:

1/x + 1/(x+6) = 1/4

(2x+6)/(x(x+6)) = 1/4
4(2x+6)=x(x+6)
x² -2x -24 = 0
Solve for x (reject the negative root).
The large one will fill in x hours alone, and the small one, x+6 hours.

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