Chapter 12.8, Problem 4P

To determine

To calculate: The number of persons needed to do a job varies directly as the amount of work to do done and inversely as the time in which the job must be done.

if $3$ peoples can mow $300m^2$ of grass in $0.5h$ days, how long will it take $7$ people to mow $700m^2$ .

Answer to Problem 4P

The people mow grass in $5$hours.

Explanation of Solution

Given information:

The number of persons needed to do a job varies directly as the amount of work to do done and inversely as the time in which the job must be done.

if $3$ peoples can mow $300m^2$ of grass in $0.5h$ days, how long will it take $7$ people to mow $700m^2$

Formula used:

The formula for people area:

  $people=\frac{area}{heigh}$

For varies jointly:

  $\frac{P_1{H}_1}{A_1}=\frac{P_2{H}_2}{A_2}$

Calculation:

The number of persons needed to do a job varies directly as the amount of work to do done and inversely as the time in which the job must be done.

if $3$ peoples can mow $300m^2$ of grass in $0.5h$ days, how long will it take $7$ people to mow $700m^2$

Recall that to find the area:

  $people=\frac{area}{heigh}$

For varies jointly:

  $\frac{P_1{H}_1}{A_1}=\frac{P_2{H}_2}{A_2}$

Therefore, the given area by,

  $\begin{array}{c}\frac{3\times 0.5}{300}=\frac{M_2\times 7}{7000}\\ 3\times 0.5\times 7000=M_2\times 300\times 7\\ M_2=\frac{3\times 0.5\times 700}{300\times 7}\\ M_2=\frac{3\times 0.5\times 1000}{300}\end{array}$

Then the height is:

  $\begin{array}{c}{M}_2=\frac{3\times 0.5\times 1000}{300}\\ M_2=0.5\times 10\\ M_2=5\end{array}$

Thus, the mow area grass in: $5\text{hours}$ .