Vincen wrote: ↑

Thu Sep 03, 2020 5:26 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

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

Vincen wrote: ↑

Thu Sep 03, 2020 5:26 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

Answer: A

Source: Official Guide

Solution:

Let t = the number of hours Bob had walked when he and Yolanda met. Thus, Yolanda had walked for (t + 1) hours. We can create the equation:

3(t + 1) + 4t = 45

3t + 3 + 4t = 45

7t = 42

t = 6

Since Bob’s rate was 4 mph, and he had walked for 6 hours, he had walked 4 x 6 = 24 miles when he and Yolanda met.

Answer: A