Chapter 8.2, Problem 54PPS

a.

To determine

To find: the expression that represents the time spent at faster pace.

Answer to Problem 54PPS

The expression is $t=\frac{10}{x}$ .

Explanation of Solution

Given information:

Cameron is taking a $20$ -mile kayaking trip and travels half the distance at one rate and the rest of the distance travels $2$ miles per hour slower.

Calculation: let $x$ represents the faster pace in miles per hour,

To find the expression that represents the time spent at that pace, use the speed formula,

  $\begin{array}{l}t=\frac{20}{2x}\\ t=\frac{10}{x}\text{ [divide]}\end{array}$

Thus, the expression is $t=\frac{10}{x}$ .

b.

To determine

To find: the expression that represents the time spent at slower pace.

Answer to Problem 54PPS

The expression is $t=5$ .

Explanation of Solution

Given information:

Cameron is taking a $20$ -mile kayaking trip and travels half the distance at one rate and the rest of the distance travels $2$ miles per hour slower.

Calculation: since, at slower pace the speed is $2$ miles per hour,

To find the expression that represents the time spent at slower pace, use the speed formula,

  $\begin{array}{l}t=\frac{20}{2·2}\\ t=5\text{ [divide]}\end{array}$

Thus, the expression is $t=5$ .

c.

To determine

To find: the expression that represents the total amount of time that Cameron needed to complete the trip.

Answer to Problem 54PPS

The expression is $T=\frac{10+5x}{x}$ that represents the total amount of time that Cameron needed to complete the trip.

Explanation of Solution

Given information:

Cameron is taking a $20$ -mile kayaking trip and travels half the distance at one rate and the rest of the distance travels $2$ miles per hour slower.

Calculation: to find the total amount of time, add the faster pace time and slower pace time,

  $\begin{array}{l}T=\frac{10}{x}+5\\ T=\frac{10+5x}{x}\text{ [simplify]}\end{array}$

Thus, the expression is $T=\frac{10+5x}{x}$ .