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?
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To find out how long it would take hose B to fill the pool, we need to first determine how much work hose A does in 1 hour.
Since hose A takes 10 hours to fill the pool, we can say that in 1 hour, hose A fills 1/10th of the pool.
Now, let's consider the combined effort of hoses A and B together. We know that together they can fill the pool in 6 hours. This means that in 1 hour, hoses A and B together fill 1/6th of the pool.
To find how much work hose B does in 1 hour, we subtract the work of hose A from the combined work of both hoses:
1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15
This means that hose B alone can fill 1/15th of the pool in 1 hour.
Therefore, it would take hose B alone 15 hours to fill the pool.