swerve wrote: ↑Mon Jun 01, 2020 5:25 am
Guy drives 60 miles to attend a meeting. Halfway through, he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half. His average speed for the entire trip is 30 miles per hour. Guy drives on average how many miles per hour during the first half of the way?
A. 12
B. 14
C. 16
D. 24
E. 40
The OA is
D
Source: Economist GMAT
Solution:
We can let the rate for the first half of the trip = r and the rate for the second half = r + 16. We also know that the distance for the first half = 30 and for the second half = 30. Thus, the time for the first half is 30/r and the time for the second half is 30/(r + 16).
Let’s now determine r:
average = (total distance)/(total time)
30 = 60/(30/r + 30/(r + 16))
Let’s solve r by dividing the numerator and denominator by 30:
30 = 2/[(1/r) + 1/(r + 16)]
30[(1/r) + 1/(r + 16] = 2
15(1/r + 1/(r + 16) = 1
15/r + 15/(r + 16) = 1
Let’s multiply both sides by r(r + 16):
15(r + 16) + 15r = r(r + 16)
15r + 240 + 15r = r^2 + 16r
r^2 - 14r - 240 = 0
(r + 10)(r - 24) = 0
r = -10 or r = 24
Since r can’t be negative, r = 24.
Answer: D
