Chapter 12.8, Problem 3P

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 $5$ students in a typing pool can type $280$ pages in $2$ days, how many students will be needed to type $2100$ pages in $3$ days.

Answer to Problem 3P

The $225$ students.

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 $5$ students in a typing pool can type $280$ pages in $2$ days, how many students will be needed to type $2100$ pages in $3$ days.

Formula used:

The formula for work and time:

  $person=\frac{work}{time}$

For varies jointly:

  $\begin{array}{c}student=\frac{pages}{days}\\ \frac{S_1{D}_1}{P_1}=\frac{S_2{D}_2}{P_2}\end{array}$

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 $5$ students in a typing pool can type $280$ pages in $2$ days, how many students will be needed to type $2100$ pages in $3$ days.

Recall that the work and time given:

  $person=\frac{work}{time}$

For varies jointly:

  $\begin{array}{c}student=\frac{pages}{days}\\ \frac{S_1{D}_1}{P_1}=\frac{S_2{D}_2}{P_2}\end{array}$

Therefore, volume of pyramid is given by,

  $\begin{array}{c}\frac{5\times 2}{280}=\frac{S_2\times 3}{2100}\\ 10\times 2100=S_2\times 3\times 280\\ S_2=\frac{3\times 280}{10\times 2100}\\ S_2=\frac{3\times 28}{2100}\end{array}$

Then the height is:

  $\begin{array}{l}{S}_2=\frac{3\times 28}{2100}\\ S_2=225\end{array}$

Thus, the number of students are: $225$ .