Chapter 7.8, Problem 3P

To determine

To find: the work done by both jake and Maura in $2.5$ hour and $\text{h}$ hour.

Answer to Problem 3P

The work done of both in $2.5$ hours is $\frac{9}{16}$ and that of work done in $\text{h}$ hours is $\frac{\text{9h}}{\text{40}}$.

Explanation of Solution

Given:

Jakes work rate is $\frac{1}{10}$ per hour and Maura’s work rate is $\frac{1}{8}$ per hour.

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:

Jakes work rate is $\frac{1}{10}$ per hour and Maura’s work rate is $\frac{1}{8}$ per hour. In $2.5$ hours it can get:

  $\frac{2.5}{10}+\frac{2.5}{8}=\frac{1}{4}+\frac{5}{16}=\frac{9}{16}$.

In $\text{h}$ hours it can get:

  $\frac{\text{h}}{\text{10}}\text{+}\frac{\text{h}}{\text{8}}\text{=}\frac{\text{9h}}{\text{40}}$.

Hence the work done of both in $2.5$ hours is $\frac{9}{16}$ and that of work done in $\text{h}$ hours is $\frac{\text{9h}}{\text{40}}$.