Walking from X to Y

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sat Oct 10, 2015 4:51 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

Please explaing thoroughly and what is the quickest approach.

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Source: Beat The GMAT — Problem Solving | Sat Oct 10, 2015 4:51 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Oct 10, 2015 5:58 am

oquiella 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

Since Yolanda's rate = 3 mph, the distance traveled by Yolanda in the first hour = rt = 3*1 = 3 miles.
Of the 45 total miles between X and Y, the remaining distance between Bob and Yolanda = 45-3 = 42 miles.

After the first hour, Bob and Yolanda WORK TOGETHER to cover the remaining 42 miles between them.
When people work together, ADD THE RATES.
Combined rate for Bob and Yolanda = 3+4 = 7 mph.

Implication:
Every hour Bob and Yolanda together cover 7 miles.
Since Bob's rate = 4 mph, Bob will travel 4 of every 7 miles that Bob and Yolanda cover together.
Thus, Bob will travel 4/7 of the remaining 42 miles between Bob and Yolanda:
(4/7)(42) = 24 miles.

The correct answer is A.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Oct 10, 2015 6:47 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

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]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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