Chapter 7.8, Problem 4P

To determine

To find: the pipe drains in 2 hours and x hour.

Answer to Problem 4P

The pipe drain in $2$ hours is $1$ pool and the pipe drain in $\text{x}$ hours is $\frac{\text{x}}{\text{2}}$ pool.

Explanation of Solution

Given:

The work rate of the first pipe is $\frac{1}{6}$ per hour and work rate of the second pipe is $\frac{1}{3}$.

Concept used:

Rate of the work:

Ratio of work to the time interval with changes in time rate of work will change.

  $\text{work rate=}\frac{\text{work done}}{\text{time}}$.

  $\text{work rate}\times \text{time=workdone}$.

Calculation:

The work rate of the first pipe is $\frac{1}{6}$ per hour and work rate of the second pipe is $\frac{1}{3}$.

In $2$ hours the pipe can drain:

  $\frac{2}{6}+\frac{2}{3}=\frac{1}{3}+\frac{2}{3}=1$ pool.

In $\text{x}$ hours it can drain:

  $\frac{\text{x}}{\text{6}}\text{+}\frac{\text{x}}{\text{3}}\text{=}\frac{\text{3x}}{\text{6}}\text{=}\frac{\text{x}}{\text{2}}$ of pool.

Hence the pipe drain in $2$ hours is $1$ pool and the pipe drain in $\text{x}$ hours is $\frac{\text{x}}{\text{2}}$ pool.