Chapter 11, Problem 18STP

(a)

To determine

Find the situation represent a direct or inverse variation.

Answer to Problem 18STP

The situation represents the inverse variation.

Explanation of Solution

Given:

A cyclist travels from Centerville to Springfield in 2.5 hours. If she increases her speed, she can make the trip in 2 hours.

Does this situation represent a direct or inverse variation?

Concept Used:

In direct variation, as one number increases, so does the other. This is also called direct proportion: they're the same thing. An example of this is relationship between age and height.

In inverse variation, it's exactly the opposite: as one number increases, the other decreases.

As the speed is increasing and time is decreasing, it is inverse variation.

Thus, the situation represents the inverse variation.

(b)

To determine

Find the speed be to make the trip from Centerville to Springfield in 2 hours

Answer to Problem 18STP

Speed = 15 miles / hour

Explanation of Solution

Given:

A cyclist travels from Centerville to Springfield in 2.5 hours. If she increases her speed, she can make the trip in 2 hours.

If the trip from Centerville to Springfield takes 2.5 hours when travelling at 12 miles per hour, what must be the speed be to make the trip in 2 hours?

Concept Used:

  $\text{Distance}=\text{speed}·\text{time}$ and $\text{Speed}\text{=}\frac{\text{Distance}}{\text{Time}}$

Calculation:

  $\begin{array}{l}\text{Distance}=\text{Speed}·\text{Time}\\ \text{Speed}=12\text{miles/hour;}\text{Time}\text{=}\text{2}\text{.5}\text{hours}\text{.}\\ \text{Distance}=\text{12}·\text{2}\text{.5}=30\text{miles}\end{array}$

The distance between Centerville to Springfield is 30 miles.

  $\begin{array}{l}\text{Distance}=30\text{miles;}\text{Time}\text{=}\text{2}\text{hours}\\ \text{Speed}\text{=}\frac{\text{Distance}}{\text{Time}}=\frac{30}{2}=15\text{miles/hour}\end{array}$

Thus, the speed should be 15 miles / hour to complete the journey from Centerville to Springfield in 2 hours.