Chapter 8.4, Problem 62S

a.

To determine

To calculate:

The average rate of change in the distances of Mr. and Mrs. Wells from home between 1 and 3 hours after leaving home

Answer to Problem 62S

The average rate of change in distances of Mr. and Mrs. Wells between 1 and 3 hours after leaving home is $55\text{ meter}$

Explanation of Solution

Given information:

Mr. and Mrs. Wells are taking their daughter to college. Their distances after various amount of time are,

Distance after 0 hour is 0

Distance after 1 hour is 55 meter

Distance after 2 hours is 110 meter

Distance after 3 hours is 165 meter

Distance after 4 hours is 165 meter

Distance after 5 hours is 225 meter

Calculation:

The average rate of change in distances between 1 and 3 hours can be calculated as,

  $\begin{array}{l}\frac{55+110+165}{1+2+3}\\ =\frac{330}{6}\\ =55\text{ meter}\end{array}$

Therefore, the average rate of change in distances between 1 and 3 hours of Mr. and Mrs. Wells after leaving home is $55\text{ meter}$

b.

To determine

To calculate:

The average rate of change in the distances of Mr. and Mrs. Wells from home between 0 and 5 hours after leaving home

Answer to Problem 62S

The average rate of change in distances between 0 and 5 hours of Mr. and Mrs. Wells after leaving home is $48\text{ meter}$

Explanation of Solution

Given information:

Mr. and Mrs. Wells are taking their daughter to college. Their distances after various amount of time are,

Distance after 0 hour is 0

Distance after 1 hour is 55 meter

Distance after 2 hours is 110 meter

Distance after 3 hours is 165 meter

Distance after 4 hours is 165 meter

Distance after 5 hours is 225 meter

Calculation:

The average rate of change in distances between 1 and 3 hours can be calculated as,

  $\begin{array}{l}\frac{0+55+110+165+165+225}{0+1+2+3+4+5}\\ =\frac{720}{15}\\ =48\text{ meter}\end{array}$

Therefore, the average rate of change in distances between 0 and 5 hours of Mr. and Mrs. Wells after leaving home is $48\text{ meter}$