Question

A 2-column table with 3 rows. Column 1 is labeled time elapsed (hours) with entries 2, 4, 7. Column 2 is labeled Distance Run (miles) with entries 13.5, 27.5, 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 or slow down?

Answer 1

To find Larry's average speed during the specified time intervals, we can use the formula for average speed:

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

### From Hour 2 to Hour 4

1. **Distance at 2 hours:** 13.5 miles
2. **Distance at 4 hours:** 27.5 miles

**Total Distance from hour 2 to hour 4:**

\[
\text{Distance} = \text{Distance at 4 hours} - \text{Distance at 2 hours} = 27.5 \, \text{miles} - 13.5 \, \text{miles} = 14 \, \text{miles}
\]

**Total Time from hour 2 to hour 4:**

\[
\text{Time} = 4 \, \text{hours} - 2 \, \text{hours} = 2 \, \text{hours}
\]

**Average Speed from hour 2 to hour 4:**

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

### From Hour 4 to Hour 7

1. **Distance at 4 hours:** 27.5 miles
2. **Distance at 7 hours:** 48.5 miles

**Total Distance from hour 4 to hour 7:**

\[
\text{Distance} = \text{Distance at 7 hours} - \text{Distance at 4 hours} = 48.5 \, \text{miles} - 27.5 \, \text{miles} = 21 \, \text{miles}
\]

**Total Time from hour 4 to hour 7:**

\[
\text{Time} = 7 \, \text{hours} - 4 \, \text{hours} = 3 \, \text{hours}
\]

**Average Speed from hour 4 to hour 7:**

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

### Summary

- **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 from both intervals are the same (7 miles per hour), **Larry did not speed up or slow down**; his speed remained constant.