The police have accused a driver of breaking the speed limit of 55 miles per hour. As proof, they provide two photographs. One photo shows the driver's car passing a toll booth at exactly 4:00 PM. The second photo shows the driver's car passing another toll booth 21 miles down the highway at exactly 4:20 PM. Does the photo evidence prove that the driver broke the speed limit during this time? Answer by determining the driver's average speed. Round the average speed to the nearest whole number.

To determine whether the driver broke the speed limit, we first need to calculate the average speed over the distance between the two toll booths.

### Step 1: Calculate Time Taken
The two photographs provide timestamps:
- Time at the first toll booth: 4:00 PM
- Time at the second toll booth: 4:20 PM

The time difference between 4:00 PM and 4:20 PM is:
\[
\text{Time Taken} = 20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours}
\]

### Step 2: Calculate Average Speed
The driver traveled 21 miles in \(\frac{1}{3}\) hours. To find the average speed, we use the formula:
\[
\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{21 \text{ miles}}{\frac{1}{3} \text{ hours}} = 21 \times 3 = 63 \text{ miles per hour}
\]

### Step 3: Compare with the Speed Limit
The speed limit is 55 miles per hour. The calculated average speed is 63 miles per hour.

### Conclusion:
Since the driver's average speed is 63 miles per hour, which exceeds the speed limit of 55 miles per hour, the photo evidence suggests that the driver was speeding during the time between the two toll booths.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How could the driver argue that the speed was not consistently over the limit?
2. What assumptions are made in using average speed to prove speeding?
3. What would the average speed be if the time was 25 minutes instead of 20 minutes?
4. Can you calculate the speed if the driver had traveled 30 miles in 40 minutes?
5. How does instantaneous speed differ from average speed in this context?

**Tip**: Always check if the time or distance data involves rounding, as it can affect the accuracy of calculations.

Determine whether a driver exceeded the speed limit of 55 mph by calculating their average speed over 21 miles in 20 minutes. This problem involves key mathematical concepts like speed, distance, and time calculations, and is suitable for students in Grades 6-8.

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