An auto race consists of 8 laps. A driver completes the first 3 laps at an average speed of 185 miles/hour and the remaining laps at an average speed of 200 miles/hour. If d represents the length of one lap, which expression represents the time in hours,t, that it takes the driver to complete the race?

Question

anonymous · Answer

You must calculate time for the varying speeds. Physically, you know that velocity * time = distance, rewritten:
t= d/v.

In part 1 of the race, the distance that the driver covers is 3 laps, which has a distance of 3d. The average velocity is 185 mi/hr, thus, in the first 3 laps, 
t1= 3d/185.

In part 2 of the race, the average speed now increases but the distance per lap stays the same (naturally). Again, the distance for 5 laps is 5d.
t2 = 5d/200.

thus, the total time is t = t1 + t2.