One hour after Yolanda started walking from \(X\) to \(Y,\) a distance of \(45\) miles, Bob started walking along the

[Vincen]

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

Answer: A

Source: Official Guide

[Brent@GMATPrepNow]

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

Answer: A

Source: Official Guide

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)
= 24 miles

Answer: A