Chapter 7.8, Problem 13P

To determine

Tofind:the duration of each machine to do the job alone.

Answer to Problem 13P

It will take $4\frac{1}{2}$ hours for faster machine to do job and $\text{9}$ hours for slower machine to do job.

Explanation of Solution

Given:

One printer work as twice as fast as other.

When both are used it can print a magazine in $3$ hours.

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 the speed of the faster printer and $\text{2x}$ is the slower printer.

  $\frac{\text{3}}{\text{x}}\text{+}\frac{\text{3}}{\text{2x}}\text{=1}$ .

Combining like terms:

  $\frac{\text{9}}{\text{2x}}\text{=1}$ .

Multiplying both side by $\text{x}$ write the answer in mixed number:

  $\text{x=}\frac{9}{2}=4\frac{1}{2}$ .

  $\text{2x=2×}\frac{\text{9}}{\text{2}}\text{=9}$ .

Hence, it will take $4\frac{1}{2}$ hours for faster machine to do job and $\text{9}$ hours for slow machine to do job.