Chapter 7.8, Problem 14P

To determine

Tofind:the total duration of Arthur, Bonnie and Claire by working together.

Answer to Problem 14P

It will take $13\frac{1}{3}$ minute working together.

Explanation of Solution

Given:

Arthur can do job in $\text{30}$ min.

Bonnie can do it in $\text{40}$ min.

Claire can do it in $\text{60}$ min.

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 equation where $\text{x}$ is amount of time in working together.

  $\frac{\text{x}}{30}\text{+}\frac{\text{x}}{40}\text{+}\frac{\text{x}}{60}\text{=1}$ .

Combining like terms:

  $\text{0}\text{.075x=1}$ .

Dividing both side by $\text{0}\text{.075}$ :

  $\text{x=}\frac{1}{0.075}$ .

  $x=13\frac{1}{3}$ .

Hence, it will take $13\frac{1}{3}$ minute working together.