Question

Fill in the blanks!
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? _ (7 mph, 6.75 mph, 13.5 mph)
What was his average speed from hour 4 to hour 7? _ (5 mph, 7 mph, 9.7 mph)
Did he speed up, slow down, or stay the same? _ (Speed up, Slow down, stay the same)

Answer 1

To find Larry's average speed over the different 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:

- At 2 hours, the distance is 13.5 miles.
- At 4 hours, the distance is 27.5 miles.

**Total Distance:**
\[
27.5 \text{ miles} - 13.5 \text{ miles} = 14 \text{ miles}
\]

**Total Time:**
\[
4 \text{ hours} - 2 \text{ hours} = 2 \text{ hours}
\]

**Average Speed:**
\[
\text{Average Speed} = \frac{14 \text{ miles}}{2 \text{ hours}} = 7 \text{ mph}
\]

So, the average speed from hour 2 to hour 4 is **7 mph**.

---

### From hour 4 to hour 7:

- At 4 hours, the distance is 27.5 miles.
- At 7 hours, the distance is 48.5 miles.

**Total Distance:**
\[
48.5 \text{ miles} - 27.5 \text{ miles} = 21 \text{ miles}
\]

**Total Time:**
\[
7 \text{ hours} - 4 \text{ hours} = 3 \text{ hours}
\]

**Average Speed:**
\[
\text{Average Speed} = \frac{21 \text{ miles}}{3 \text{ hours}} = 7 \text{ mph}
\]

So, the average speed from hour 4 to hour 7 is **7 mph**.

---

### Summary of Results:
- Average speed from hour 2 to hour 4: **7 mph**
- Average speed from hour 4 to hour 7: **7 mph**

### Did he speed up, slow down, or stay the same?
Since Larry's average speed from hour 2 to hour 4 (7 mph) is the same as his speed from hour 4 to hour 7 (7 mph), we conclude that he **stayed the same**.

### Final Answers:
1. Average speed from hour 2 to hour 4: **7 mph**
2. Average speed from hour 4 to hour 7: **7 mph**
3. Speed change: **Stay the same**