deepak123gmat wrote:A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per
hour. At what average speed must the driver complete the remaining 20 miles to achieve
an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver
did not make any stops during the 40-mile trip.)
A. 65 mph
B. 68 mph
C. 70 mph
D. 75 mph
E. 80 mph
We could plug in the answer choices, which represent the speed for the remaining 20 miles.
The correct answer must be more than 70. If we travel for 20 miles at 70 mph after traveling the first 20 miles at 50 miles per hour, the average for the whole trip will not be (50+70)/2 = 60 (the number right in the middle) because
we won't spend the same amount of time traveling at each speed. Since we'll spend more time traveling at 50mph than we'll spend traveling at 70mph, the average for the whole trip will be closer to 50 than to 70. Thus, in order for the average for the whole trip to be 60, we must travel faster than 70mph for the remaining 20 miles. Eliminate A, B and C.
Let's try answer choice D:
d/r = 20/75 = 4/15 hour for the remaining 20 miles
d/r = 20/50 = 2/5 hour for the first 20 miles
Total time = 4/15 + 2/5 = 10/15 = 2/3 hour
Total distance = 20+20 = 40 miles
Average speed = d/t = 40/(2/3) = 60mph
The correct answer is D.
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