chieftang wrote:Simon traveled between two cities. For the first half of the trip, he drove at a constant rate of X miles per hour. Over the entire trip he averaged a rate of T miles per hour. What was his rate of travel for the second half of his trip in terms of X and T, assuming it was constant?
(A) T - (X/2)
(B) 2T - (X/2)
(C) 2TX / (X-T)
(D) TX / (2X-2T)
(E) X / ((2X/T)-1)
Source: Original 700 level question
Let the distance = 24 miles.
Let X = 4 miles per hour.
Time for the first half of the trip = d/r = 12/4 = 3 hours.
Let the rate for the second half of the trip = 12 miles per hour.
Time for the second half of the trip = d/r = 12/12 = 1 hour.
T = average speed for the whole trip = total distance/total time = 24/(3+1) = 6 miles per hour.
Since the question asks for the rate during the second half of the trip, our target is 12.
Now we plug X=4 and T=6 into the answers to which yields our target of 12.
Only answer choice
E works:
X/((2X/T) - 1) = 4/((2*4)/6 - 1) = 4/(1/3) = 12.
The correct answer is
E.
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