Chapter 8.3, Problem 16MCQ

a.

To determine

To write: an expression that represents the time spent at that pace

Answer to Problem 16MCQ

The expression that represents the time spent at that pace is $\frac{50}{x}$

Explanation of Solution

Given information: The question is

Lucita is going to a beach $100$ miles away. She travels half the distance at one rate. The rest of the distance, she travels $15$ miles per hour slower if $x$ represents the faster pace in miles per hour

Calculation:

  $\begin{array}{l}d=rt\\ 50=xt\\ t=\frac{50}{x}\end{array}$

Distance is rate multiplied by time. She travels half the distance $50\text{ miles}$ at a rate of $x$

b.

To determine

To write: an expression for the amount of time spent at the slower pace

Answer to Problem 16MCQ

The expression for the amount of time spent at the slower pace is $\frac{50}{x-15}$

Explanation of Solution

Given information: The question is

Lucita is going to a beach $100$ miles away. She travels half the distance at one rate. The rest of the distance, she travels $15$ miles per hour slower

Calculation:

  $\begin{array}{l}d=rt\\ 50=\left(x-15\right)t\\ t=\frac{50}{x-15}\end{array}$

Distance is rate multiplied by time. She travels half the distance $50\text{ miles}$ at a rate of $15\text{ miles}$ slower than her faster rate of $x$

c.

To determine

To write: an expression for the amount of time Lucita needed to complete the trip

Answer to Problem 16MCQ

The expression for the amount of time Lucita needed to complete the trip is $\frac{50}{x}+\frac{50}{x-15}$

Explanation of Solution

Given information: The question is

Lucita is going to a beach $100$ miles away. She travels half the distance at one rate. The rest of the distance, she travels $15$ miles per hour slower

Calculation:

The total time needed equals the time spent during the first needed for the second half

  $\begin{array}{l}{\text{t}}_{total}=t_1+t_2\\ {\text{t}}_{total}=\frac{50}{x}+\frac{50}{x-15}\end{array}$