Chapter 11.4, Problem 5P

To determine

The expression that represent the total time in hours riding out and back.

Answer to Problem 5P

  $\frac{45}{4r}$

Explanation of Solution

Given information:

A bicyclist rides 5 miles out and then rides back. His speed returning back is reduced by 20% because of rain. Let his speed going out be r miles per hour.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let the speed of bicyclist going out be r miles per hour. So, the speed returning back would be $0.8r$ as it is reduced by 20% than the speed of going out.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time riding out + Time returning back}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed going out}}+\frac{\text{Distance traveled}}{\text{Speed returning back}}\\ =\frac{5}{r}+\frac{5}{0.8r}\\ =\frac{4+5}{0.8r}\\ =\frac{9}{0.8r}\\ =\frac{90}{8r}\\ =\frac{45}{4r}\end{array}$

Thus, the expression for total time is $\frac{45}{4r}$ .