Question

8. The larger of two hoses can fill a pool in 6 hours. The smaller hose can fill the same pool in 8 hours. If both hoses are used, what fraction of the pool will be filled in 2 hours?A. 1/4B.1/7 C. 3/4 D. 7/12

Answer 1

Inverse Proportions

A pool will be filled with two hoses. The larger hose can fill it in 6 hours and the smaller hose can do it in 8 hours.

Let's calculate the fraction of the pool that both hoses fill in one hour.

Since the larger hose fills the pool in 6 hours, in one hour it fills 1/6 of the pool.

The smaller hose needs 8 hours to fill the pool, so in one hour it fills 1/8 of the pool.

Working together, the total fraction of the pool filled is:

`(1)/(6)+(1)/(8)`

The LCM of the denominators is 24, thus the sum of the fractions is:

`(1)/(6)+(1)/(8)=(4)/(24)+(3)/(24)=(7)/(24)`

That is the fraction of the pool filled by both hoses in one hour. In two hours it will be double:

`2\cdot(7)/(24)=(7)/(12)`

We must select option D. 7/12