A cyclist bikes x distance at 10 miles per hour and returns over the same path at 9 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?	Choose the correct choice from the following: A) 8.1 B) 8.3 C) 8.6 D) 8.9 E) 9.5

Rationale: "distance = d 1 = x miles speed = s 1 = 10 miles per hour time = t 1 = distance / speed = x / 10 2 . going from b to a distance = d 2 = x miles speed = s 2 = 9 miles per hour time = t 2 = distance / speed = x / 9 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 9 = x ( 1 / 10 + 1 / 9 ) = x ( 4 + 5 ) / 40 = 19 x / 90 speed = 2 x / ( 19 x / 90 ) = ( 2 x * 90 ) / 9 x = 180 x / 19 x = 180 / 19 = 9.5 answer : e"
Answer: E