Chapter 8.5, Problem 21PPS

a.

To determine

To write an equation.

Answer to Problem 21PPS

The equation is related as $s=\frac{48}{t}$

Explanation of Solution

Given information:

12 students were able to distribute 1000 flyers in four hours.

Write an equation that relates the number of students ‘s’ to the amount of time ‘t’ it take to distribute 1000 flyers.

Calculation:

The equation can be obtained as

When more students help, less time to needed to distribute 1000 flyers

Since, students varies inversely as time

Therefore,

  $\begin{array}{l}s=\frac{k}{t}\left[\begin{array}{l}s=\text{student}\\ t=\text{time}\\ k=\text{constant}\end{array}\right]\\ st=k\end{array}$

Put the values of $s=1000\text{ and }t=\text{4 in above equation }\left[\begin{array}{l}\text{students=1000}\\ \text{time=4hours}\end{array}\right]$

  $\begin{array}{l}k=12*4\\ k=48\end{array}$

Hence,

The equation is related as $s=\frac{48}{t}$

b.

To determine

To find out the time when 15 students to hand out the same number of flyers this year.

Answer to Problem 21PPS

The value of $t\text{ is 3}\text{.2 hours}$

Explanation of Solution

Given information:

How long would it take 15 students to hand out the same number of flyers this year

Calculation:

The time can be obtained as when 15 students to hand out the same number of flyers this year.

Since we find out $s=\frac{48}{t}$ in previous part

Put $s=15\left[s\text{=students}\right]$

Therefore

  $\begin{array}{l}15=\frac{48}{t}\\ t=\frac{48}{15}\\ t=3.2\text{ hours}\end{array}$

Hence,

The value of $t\text{ is 3}\text{.2 hours}$