A cyclist bikes x distance at 12 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
Choose the correct answer.
A) 8.1
B) 8.3
C) 9.6
D) 8.9
E) 9.0

Rationale: "distance = d 1 = x miles speed = s 1 = 12 miles per hour time = t 1 = distance / speed = x / 12 2 . going from b to a distance = d 2 = x miles speed = s 2 = 8 miles per hour time = t 2 = distance / speed = x / 8 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : c"
Answer: C