AAPL wrote:Two trains started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at constant rate, completed the 100-mile trip in 5 hours; train Y, traveling at constant rate, completed the 100-mile trip in 3 hours. How miles had X traveled when it met train Y?
A. 37.5
B. 40.0
C. 60.0
D. 62.5
E. 77.5
Time and rate have a RECIPROCAL RELATIONSHIP.
If Mary works TWICE as fast as John, Mary's time will be 1/2 John's time.
If Mary works THREE TIMES as fast as John, Mary's time will be 1/3 John's time.
The time ratio for X and Y is as follows:
(X's time) : (Y's time) = 5 hours : 3 hours = 5:3.
Thus, the rate ratio for X and Y is the RECIPROCAL of the time ratio:
(X's rate) : (Y's rate) = 3:5.
The rate ratio implies the following:
Of every 8 miles that are traveled when X and Y move toward each other, X travels 3 miles, while Y travels 5 miles.
Since X travels 3 of every 8 miles, X will travel 3/8 of the 100 miles between the two trains:
X's distance = (3/8) * 100 = 37.5 miles.
The correct answer is
A.
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