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 300 miles per hour and the train's average speed when traveling from point Y to point Z was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z? Choices.
A) 200	B) 220	C) 240	D) 180	E) 260

Rationale: average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 300 speed y - z = 100 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 / 300 ) + ( d / 100 ) 3 d / ( 2 d / 300 ) + ( 3 d / 300 ) 3 d / ( 5 d / 300 ) 900 d / 5 d average speed = 180 answer : d
Answer: D