Hoses A and B together can fill a swimming pool in 6 hours. If hose A alone takes 10 hours to fill the pool, how long would it take hose B to fill the pool?

1/10 + 1/B = 1/6

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To find out how long it would take hose B to fill the pool, we first need to determine how efficiently each hose fills the pool.

Let's assume that the pool requires a certain amount of water to be filled, which we'll call 'x'.

Therefore, in one hour, hose A can fill 1/10th of the pool (Let's call it '1/10x').

If hoses A and B are working together, they can fill the pool in 6 hours. So, in one hour, together they can fill 1/6th of the pool (Let's call it '1/6x').

To find out how efficient hose B is, we need to subtract the efficiency of hose A from the combined efficiency of hoses A and B.

So, the efficiency of hose B is given by: (efficiency of A and B) - (efficiency of A)

Efficiency of A and B = 1/6x
Efficiency of A = 1/10x

Therefore, the efficiency of hose B = (1/6x) - (1/10x)

To simplify this expression, we need to find the common denominator for 6 and 10, which is 30.

So, the efficiency of hose B = (5/30x) - (3/30x) = 2/30x = 1/15x

This means that hose B can fill 1/15th of the pool in one hour.

Now we can determine how long it would take hose B alone to fill the pool by taking the reciprocal of its efficiency:

Time taken by hose B alone = 1 / (1/15x) = 15 hours

Therefore, hose B alone would take 15 hours to fill the pool.