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Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?
(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000
(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000
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10 Dec 2007, 15:21
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I get B. Let's call d the total distance from A to B. Then the average speed can be represented as d/time. Further, the time can be represented as the sum of the time spent at 60 mph and the time spent at 50 mph, where time = distance/rate. So the time is:
xd/60 + (1-x)d/50, and the overall equation for average speed is:
speed = d/[xd/60 + (1-x)d/50]. To simplify, first find a common denominator for the two time components:
xd/60 + (1-x)d/50 = 5xd/300 + 6(1-x)d/300 = (6d-xd)/300. So,
speed = d/[(6d-xd)/300]. Rewrite as
speed = d * 300/(6d-xd) = 300/(6-x). So the numerator is 300.
