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

Answer:

The correct option is C.

Step-by-step explanation:

It is given that at noon the pool was 1/3 full and $1\frac{1}{4}$ hours later it was 3/4 full.

Total parts of pool filled in $1\frac{1}{4}$ hours is

$\frac{3}{4}-\frac{1}{3}=\frac{9-4}{12}=\frac{5}{12}$

The time can be written as

$1\frac{1}{4}=\frac{5}{4}$

It means $\frac{5}{12}th$ part of the pool is filled in $\frac{5}{4}$ hours.

Let the pool is filled completely in x hours. So $\frac{5}{12}th$ part of the pool is filled is $\frac{5x}{12}$.

$\frac{5x}{12}=\frac{5}{4}$

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.