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.

Question

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.