Question

Time Elapsed (hr) - Distance Run (mi)
2 - 13.5
4 - 27.5
7 - 48.5

Larry recorded his time as he ran.
What was his average speed from hour 2 to hour 4? _
What was his average speed from hour 4 to hour 7? _
Did he speed up, slow down, or stay the same?

Answer 1

To calculate Larry's average speed for the given intervals, we use the formula for average speed:

\[
\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}
\]

1. **Average speed from hour 2 to hour 4:**
- Distance at hour 2: 13.5 miles
- Distance at hour 4: 27.5 miles
- Distance traveled from hour 2 to hour 4: \(27.5 - 13.5 = 14\) miles
- Time elapsed from hour 2 to hour 4: \(4 - 2 = 2\) hours

\[
\text{Average Speed} = \frac{14 \text{ miles}}{2 \text{ hours}} = 7 \text{ miles per hour}
\]

2. **Average speed from hour 4 to hour 7:**
- Distance at hour 4: 27.5 miles
- Distance at hour 7: 48.5 miles
- Distance traveled from hour 4 to hour 7: \(48.5 - 27.5 = 21\) miles
- Time elapsed from hour 4 to hour 7: \(7 - 4 = 3\) hours

\[
\text{Average Speed} = \frac{21 \text{ miles}}{3 \text{ hours}} = 7 \text{ miles per hour}
\]

3. **Comparison of average speeds:**
- Average speed from hour 2 to hour 4: 7 miles per hour
- Average speed from hour 4 to hour 7: 7 miles per hour

Since the average speeds for both intervals are the same (7 miles per hour), we conclude that:

- Larry **stayed the same** in terms of speed between hour 2 to hour 4 and hour 4 to hour 7.