Question

A hose with a larger diameter working alone can fill a swimming pool in 9 hours.A hose with a smaller diameter working alone can fill a swimming pool in 18 hours.working together,how long would it take the two hoses to fill the swimming pool?

Answer 1

The large hose fills 1 pool in 9 hours written as  1/9

The small hose fills 1 pool in 18 hours, written as 1/18

Now you have 1/9 + 1/18 = 1/x ( x is the unknown time for both hoses).

rewrite 1/9 with a common denominator as 1/18:

1/9 = 2/18

Now you have 2/18 + 1/18 = 1/x

Add the left side:

2/18 + 1/18 = 3/18

Now you have 3/18 = 1/x

Cross Multiply:

3x = 18

Divide both sides by 3"

x = 18/3

X = 6

It will take both hoses 6 hours.