Question

A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 114114 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?A. 213213B. 223223C. 3D. 312312E. 323

Answer 1

The correct option is C.

Explanation:

It is given that at noon the pool was 1/3 full and
`1(1)/(4)` hours later it was 3/4 full.

Total parts of pool filled in
`1(1)/(4)` hours is

`(3)/(4)-(1)/(3)=(9-4)/(12)=(5)/(12)`

The time can be written as

`1(1)/(4)=(5)/(4)`

It means
`(5)/(12)th` part of the pool is filled in
`(5)/(4)` hours.

Let the pool is filled completely in x hours. So
`(5)/(12)th` part of the pool is filled is
`(5x)/(12)`.

`(5x)/(12)=(5)/(4)`

Multiply both sides by 12.

`5x=15`

Divide both sides by 5.

`x=3`

The pool is completely filled in 3 hours. Therefore the correct option is C.