Question

A graph shows time (minutes), numbered 15 to 135 on the horizontal axis, and distance from home (miles) labeled 1 to 10 on the vertical axis. The line shows an increase to 8 miles at 45 minutes, constant, and decrease at 90 minutes.
Consider the graph of Miriam's bike ride to answer the questions.

How many hours did Miriam stop to rest?

How many hours did it take Miriam to bike the initial 8 miles?

Answer 1

To analyze the graph of Miriam's bike ride, let's break down the information provided:

1. **Distance and Time**: The graph indicates that Miriam biked to 8 miles at 45 minutes. This means she spent 45 minutes biking to reach that distance.

2. **Constant Distance**: After reaching 8 miles at 45 minutes, the graph shows that Miriam maintained that distance for a period (which extends from 45 minutes to 90 minutes). This indicates she was resting during that time.

3. **Decrease in Distance**: After 90 minutes, Miriam started to decrease her distance, which likely means she was biking back home.

### Answers to the Questions:

1. **How many hours did Miriam stop to rest?**
- Miriam reached 8 miles in 45 minutes and then maintained that distance (rested) until 90 minutes. The duration of rest is:
\[
90 \text{ minutes} - 45 \text{ minutes} = 45 \text{ minutes}
\]
- To convert minutes to hours:
\[
45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}
\]

Thus, **Miriam stopped to rest for 0.75 hours**.

2. **How long did it take Miriam to bike the initial 8 miles?**
- As stated, it took Miriam 45 minutes to bike the initial 8 miles. To convert this into hours:
\[
45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}
\]

Therefore, **it took Miriam 0.75 hours to bike the initial 8 miles**.