John drives 50 miles to work each day

lheiannie07 wrote:John drives 50 miles to work each day and returns by the same route in the evening. He is able to drive only 25 miles per hour during rush hour in the morning. He decides to come home early and take advantage of the light traffic in the early afternoon. He makes it back home in half the usual rush-hour time. What is his average speed to and from work that day?

(A) 25 mph
(B) 30 1�3 mph
(C) 33 1�3 mph
(D) 37.5 mph
(E) 50 mph

Since the rush-hour speed is 25 mph, the time to travel the 50 miles during rush hour = d/r = 50/25 = 2 hours.
Time to travel the 50 miles in light traffic = 1/2 the rush-hour time = (1/2)(2) = 1 hour.
Average speed for the whole 100-mile trip = (total distance)/(total time) = 100/(2+1) = 100/3 = 33.33 mph.

The correct answer is C.

Alternate approach:

Generally, when the SAME DISTANCE on the GMAT is traveled at two different speeds, the average speed for the whole trip will be just a bit less than the AVERAGE of the lower speed and the higher speed.
The reason:
Traveling at the lower speed takes LONGER, with the result that MORE TIME is spent traveling at the lower speed than at the higher speed.
As a result, the average speed for the whole trip will be just A BIT LESS THAN THE AVERAGE of the lower speed and the higher speed.

In the problem above:
Since the trip in light traffic takes 1/2 the time of the rush-hour trip, the rate home must be TWICE the rush-hour rate of 25 mph:
2*25 = 50 mph.
Average of the lower speed and the higher speed = (25+50)/2 = 35 mph.
Thus, the average speed for the entire trip must be just a bit less than 35.

The correct answer is C.