swerve wrote:The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed in miles per hour?
A. 20
B. 30
C. 40
D. 50
E. 80
The OA is C
Source: GMAT Paper Tests
We are given that cars A and B both traveled 400 miles and that car A's average speed was 10 mph greater than that of car B. We can let the rate of car B = r and the rate of car A = r + 10.
Since both cars traveled 400 miles and time = distance/rate, the time of car A is 400/(r+10).
We are also given that it took car A 2 hours less than it took car B to travel the 400 miles. We can set up the following equation:
400/(r+10) + 2 = 400/r
Multiplying the entire equation by r(r+10), we have:
400r + 2(r)(r+10) = 400(r+10)
400r + 2r^2 + 20r = 400r + 4000
2r^2 + 20r - 4000 = 0
r^2 + 10r - 2000 = 0
(r + 50)(r - 40) = 0
r = -50 or r = 40
Since r must be positive, then r = 40.
Answer: C
