Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 100 miles per hour and the train's average speed when traveling from point Y to point Z was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z?  Pick one:  A) 90  B) 85  C) 85.5  D) 70  E) 90

Rationale: "average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 100 speed y - z = 75 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 100 ) + ( d / 75 ) 3 d / ( 6 d / 300 ) + ( 4 d / 300 ) 3 d / ( 10 d / 300 ) 900 d / 10 d average speed = 90 answer : a"
Answer: A