Chapter 11.8, Problem 31PPS

(a)

To determine

To Write: an equation relating $h,c,$ and $p$

Answer to Problem 31PPS

Therefore, the equation is $h=\frac{kp}{c}$ .

Explanation of Solution

Calculation:

The objective is to write an equation which shows how $h,c,$ and $p$ related.

The equation is written below.

  $h=\frac{kp}{c}$

Therefore, the equation is $h=\frac{kp}{c}$ .

Conclusion:

Therefore, the equation is $h=\frac{kp}{c}$ .

(b)

To determine

To find: the number of hours taken to clean the dormitory

Answer to Problem 31PPS

The number of hours taken to clean the dormitory is 4 hours

Explanation of Solution

Given:

  $8$ hours for $5$ people to clean the dormitory when there are $100$ people there.

The constant value is calculated below.

  $\begin{array}{l}h=\frac{kp}{c}\\ 8=\frac{k\left(100\right)}{5}\\ 8=20k\\ \frac{2}{5}=k\end{array}$

Now, the time is calculated below.

  $\begin{array}{l}h=\frac{kp}{c}\\ =\frac{\frac{2}{5}\left(100\right)}{10}\\ =4hours\end{array}$

Conclusion:

The number of hours taken to clean the dormitory is 4 hours