venmic wrote:Bryan and Kathleen live 150 miles apart. They each drive toward the other's house along a straight road connecting the two, Bryan at a constant rate of 30 miles per hour and Kathleen at a constant rate of 50 miles per hour. If Bryan and Kathleen leave their houses at the same time, how many miles are they from Bryan's house when they meet?
A) 40
B) 51 1/2
C) 56 1/4
D) 75
E) 93 3/4
i know the simple way of doing this but i need to know the underlying concept
please help
Approach 1: Determine what fraction of the work is performed by Bryan.
Every hour, Bryan and Kathleen travel 30+50 = 80 miles of the distance between them.
Bryan travels 30/80 = 3/8 of the distance.
Thus, he will travel 3/8 * 150 = 56.25 of the total distance.
The correct answer is
C.
Approach 2: Determine the time traveled.
Combined rate for Bryan and Kathleen = 30+50 = 80 miles per hour.
Time to travel 150 miles = d/r = 150/80 = 15/8 hours.
Distance traveled by Bryan = r*t = 30*(15/8) = 56.25 miles.
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