Chapter 8.5, Problem 45PPS

a.

To determine

To write and graph an equation relating their travel time to their average rate of speed.

Answer to Problem 45PPS

The required equation is $800=rt$

Explanation of Solution

Given information:

The distance to be travelled is 800 miles away, and time taken is inversely proportional to the average speed.

Consider r be the average speed and t be the travel time.

The required equation is

  $800=rt\left[\text{distance travelled=avg speed}\times \text{time}\right]$

The graph of the equation is

  

b.

To determine

To calculate the minimum average speed required to reach the within 18 hours.

Answer to Problem 45PPS

The average minimum speed required achieve the goal within 18 hours is $44.\overline{4}$ miles per hour.

Explanation of Solution

Given information:

The distance to be travelled is 800 miles away, and time taken is inversely proportional to the average speed. Time limit to reach the goal is 8 hours.

Formula used:

  $\text{distance travelled}=\text{avg speed}\times \text{time}$

Calculation:

To calculate the average minimum speed substitute the value of time.

  $\begin{array}{l}vt=800\\ v=\frac{800}{18}\\ v=44.\overline{4}\end{array}$

Therefore,

The average minimum speed required achieve the goal within 18 hours is $44.\overline{4}$ miles per hour.