Chapter 7.4, Problem 48E

(a)

To determine

To find: The simplified model that determines the total time taken to complete the race..

Answer to Problem 48E

Thus, the required model is $t=\frac{0.5}{r}+\frac{22}{15r}+\frac{2}{r+5}$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

Type	Distance in miles	Speed in miles per hour
Swimming	0.5	$r$
Bicycling	22	$15r$
Running	6	$r+5$

Calculation:

Consider the total time taken to complete the race is the sum for each of the event as,

  $t=\frac{0.5}{r}+\frac{22}{15r}+\frac{2}{r+5}$

(b)

To determine

To find: The time taken to complete the race if the swimming average speed is of 2 miles per hour.

Answer to Problem 48E

Thus, the total time take is of $1.84\text{hrs}$ .

Explanation of Solution

Given:

The given table is shown in Table 1

Table 1

Type	Distance in miles	Speed in miles per hour
Swimming	0.5	$r$
Bicycling	22	$15r$
Running	6	$r+5$

Calculation:

Substitute $r=2$ in the model to determine the total time taken as,

  $\begin{array}{c}t=\frac{0.5}{2}+\frac{22}{15\left(2\right)}+\frac{2}{2+5}\\ =\frac{0.2}{2}+\frac{22}{30}+\frac{6}{7}\\ =1.84\text{hrs}\end{array}$