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?

Goal is not achievable

Step-by-step 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.