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Bunuel
It takes Davis x hours to complete the Road Runners Holiday Road Race while running at R miles per hour. If it takes Hassan one hour less to complete the race, what is Hassans rate, in terms of R and x?

A. Rx/(x-1)
B. R/(2x+1)
C. R/(x-1)
D. (x-1)/R
E. (x-1)/(Rx)

Since it takes Davis x hours to complete the Road Runners Holiday Road Race while running at R miles per hour, his distance is Rx. We are also given that it takes Hassan one hour less to complete the race. So if we let H = the rate of Hassan and time of Hassan = x - 1, then his distance is H(x-1). Let’s now equate our two distances:

Rx = H(x- 1)

Rx/(x-1) = H

Answer: A
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Hi All,

This question can be solved rather easily by TESTing VALUES.

IF...
X = 2
R = 4
then Davis takes 2 hours, running 4 miles/hour, to complete the race - thus, the total distance is (2 hours)(4 mph) = 8 miles.

We're told that Hassan takes 1 less hour to complete the race, so he takes 1 hour to run the 8 miles, meaning that his rate is 8 miles per hour. So we're looking for an answer that equals 8 when X=2 and R=4. There's only one answer that matches (and you can quickly eliminate the other 4 answers without having to do too much math - IF you pay attention to how the numerators relate to the denominators...).

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Hello from the GMAT Club BumpBot!

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