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
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rohu27
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Since you want to know the detailed explanation, im giving the same.
let both meet after time t.
in t hours Bryan travels 30t miles, Kathleen=50t miles.
this should be equal to the total 150 miles.
80t=150
t=15/8
we need to find distance traveleld by Bryan: 30t=30*15/8=225/4=56 1/4
option C
let both meet after time t.
in t hours Bryan travels 30t miles, Kathleen=50t miles.
this should be equal to the total 150 miles.
80t=150
t=15/8
we need to find distance traveleld by Bryan: 30t=30*15/8=225/4=56 1/4
option C
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GMATGuruNY
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Approach 1: Determine what fraction of the work is performed by Bryan.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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venmic
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Awesome on explanation 1 - thanks
GMATGuruNY wrote:Approach 1: Determine what fraction of the work is performed by Bryan.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
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.
