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Bob & Yolanda

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by LulaBrazilia » Mon Dec 09, 2013 11:38 am
One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bob's was 4 miles per hour, how many miles had Bob walked when they met?

A. 24
B. 23
C. 22
D. 21
E. 19.5

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by Patrick_GMATFix » Mon Dec 09, 2013 11:52 am
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by Brent@GMATPrepNow » Mon Dec 09, 2013 1:16 pm
LulaBrazilia wrote:One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bob's was 4 miles per hour, how many miles had Bob walked when they met?

A. 24
B. 23
C. 22
D. 21
E. 19.5
Original length of GAP between Bob and Yolanda = 45 miles

Yolanda walks for 1 hour at a speed of 3 miles per hour.
So, Yolanda walked 3 miles during that 1 hour.
Current length of GAP between Bob and Yolanda = 42 miles

At this point, Bob starts walking.
In 1 hour, Bob walks 4 miles towards Yolanda, and Yolanda walks 3 miles towards Bob.
So, EVERY HOUR, the gap decreases a total of 7 miles.
In other words, the GAP between Bob and Yolanda SHRINKS at a rate of 7 miles per hour.

Time = distance/rate
So, time = 42/7 = 6 hours
So, it will take 6 hours for the gap to shrink from 42 miles to 0 miles.

Bob walks at a rate of 4 miles per hour.
So, Bob's travel distance = (rate)(time) = (4)(6) = [spoiler]24 miles = A[/spoiler]

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by GMATGuruNY » Mon Dec 09, 2013 3:50 pm
LulaBrazilia wrote:One hour after Yolanda started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bob's was 4 miles per hour, how many miles had Bob walked when they met?

A. 24
B. 23
C. 22
D. 21
E. 19.5

Thanks for helping
Since Yolanda's rate = 3 miles per hour, the distance traveled by Yolanda in the first hour = 3 miles.
Remaining distance between Yolanda and Bob = 45-3 = 42 miles.

When Yolanda and Bob walk toward each other, they WORK TOGETHER to cover the remaining 42 miles between them.
Since they work together, we ADD THEIR RATES.
Combined rate for Yolanda and Bob = 3+4 = 7 miles per hour.

Since 7 miles are traveled per hour, and Bob's rate is 4 miles per hour, Bob will travel 4/7 of the remaining 42 miles between him and Yolanda:
(4/7) * 42 = 24 miles.

The correct answer is A.
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