Question

Maury completed a bicycle race 1.5 hours faster than Vince at an average speed of 16 miles per hour. Vince completed the same race at an average speed of 12 miles per hour. How many miles was the race?

Answer 1

Let the time taken by Vince to complete the race was x hours. 
Maury completed the race 1.5 hours faster. This means Maury complete the race in (x - 1.5) hours.

Average Speed of Maury = 16 miles per hour
Average Speed of Vince = 12 miles per hour

Distance = Speed x Time.

For Maury:
Distance = 16(x - 1.5)

For Vince:
Distance = 12x

Since the distance covered by both was the same, we can equate the two equations as:

16(x - 1.5) = 12x
16x - 24 = 12x
4x = 24
x = 6 
This means Vince complete the race in 6 hours.

Distance = Speed x Time = 12 x 6 = 72 miles

Thus, the total distance of the race was 72 miles.