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?	Choices
A) 90 B) 85 C) 85.5 D) 70 E) 90
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   90verage 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 = 2d and let Y-Z= d   90verage speed = 3d/(2d/100) + (d/75)   3d/(6d/300) + (4d/300)   3d/(10d/300)   900d/10d   90verage speed = 90   90NSWER: 90
<result>A</result>
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?