Question

A driver intends to complete 2 laps on a track that is exactly 1 mile around at an average speed of 60 mph. He gets off to a slow start and completes the 1st lap at an average of 30 mph. How fast must he drive the second lap in order to achieve his goal?

Answer 1

Goal is not achievable

Explanation:

There are Two laps and the total distance here is 2miles. Now, it is said that he hopes to travel at a speed of 60mph, thus the total time that it would take him to complete the 2 miles distance race is 2/60 = 1/30 hours. Thus if he travels at a constant speed of 60mph he would finish the race at 1/30hours.

This means he will take a time of 1/60 hours per lap.

Now, he travels 30mph to complete 1 mile, the time taken for this is 1/30h

We now need to know the speed he travels on the second lap.

Average speed = Total distance/Total time

60mph = 2/( 1/30 + T2)

60 = 2/( (1 + 30T2)/30)

60 = 2 divided by (1 + 30T2)/30

60 = 2 * (30)/1 + 30T2

60( 1 + 30T2) = 60

1 + 30T2 = 1

30T2 = 0

T2 = 0

This means that he cannot achieve his goal again as he had taken the time meant for the whole race in a single lap.