A trucker handed in a ticket at a toll booth showing that in 2 h she had covered 159 mi on a toll road with speed limit 65 mph. The trucker was cited for speeding. Why?
First, the average speed was 159/2= 80 mph.
How could he have ever hand an average of 80 with staying in the limit of 65?
its proven by the mean value theorum f'(c)=f(b)-f(a)/(b-a)
To understand why the trucker was cited for speeding, let's break down the problem step-by-step:
Step 1: Calculate the expected distance the trucker should have covered.
Given that the trucker was driving for 2 hours on a toll road with a speed limit of 65 mph, we can calculate the expected distance using the formula: Distance = Speed × Time.
Distance = 65 mph × 2 hours = 130 miles.
Step 2: Compare the expected distance with the actual distance covered.
The ticket shows that the trucker covered 159 miles in 2 hours, which is greater than the expected distance of 130 miles. This indicates that the trucker exceeded the speed limit for at least a portion of the journey.
Conclusion: The trucker was cited for speeding because the distance covered in the given time frame exceeded the expected distance based on the speed limit.
The trucker was cited for speeding because she covered a distance of 159 miles in 2 hours, which means her average speed was 159/2 = 79.5 mph. This exceeds the speed limit of 65 mph.
To calculate the average speed, you divide the total distance traveled by the total time taken. In this case, the distance traveled was 159 miles, and the time taken was 2 hours, so the average speed is 159/2 = 79.5 mph.
Since the speed limit on the toll road was 65 mph, the trucker was going faster than the allowed speed and therefore received a speeding citation.