Question

during a gym class, jose jogged, and edwin walked at constant rates around a circular ¼ mile track. their times in minutes and distances in miles are shown in the accompanying graph.

1. at the end of 30 minutes, how many more times had jose completed the track than edwin?

1. what was jose’s average rate of jogging in miles per hour? edwin’s rate?

1. how much faster was jose jogging than edwin was walking in miles per hour?

1. how can you tell who was moving at a faster rate by looking at the graph?

Explanation:

Step1: Get 30-min distances

From the graph:

• Jose's distance at 30 min: $3$ miles
• Edwin's distance at 30 min: $1$ mile

Track length = $\frac{1}{4}$ mile

Step2: Calculate track completions

Jose's completions: $\frac{3}{\frac{1}{4}} = 3 \times 4 = 12$
Edwin's completions: $\frac{1}{\frac{1}{4}} = 1 \times 4 = 4$

Step3: Find the difference

$12 - 4 = 8$

Step4: Calculate Jose's speed (mph)

Jose goes 6 miles in 60 min (1 hour). Rate = $\frac{6}{1} = 6$ mph

Step5: Calculate Edwin's speed (mph)

Edwin goes 2 miles in 60 min (1 hour). Rate = $\frac{2}{1} = 2$ mph

Step6: Find speed difference

$6 - 2 = 4$ mph

Answer:

1. 8 more times
2. Jose's rate: 6 miles per hour; Edwin's rate: 2 miles per hour
3. 4 miles per hour
4. The steeper line on the graph represents the faster rate, which is Jose's line, so he was moving faster.