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One hour after Yolanda started walking from X to Y, a distan

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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 Bobт'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
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Sep 2013, 01:09, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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When bob starts walking The distance between them is 45-3 = 42 miles
If they meet at time t then Yolanda would have walked
X/3 minutes and Bob would have walked (42-X)/4 mins
X/3 = (42-X)/4 so X = 18
Bob would have walked 42-18 = 24 miles.

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EnterMatrix wrote:
One hour after Yolander started walking from X to Y, a distance of 45 miles, Bob started walking along the same road from Y to X. If Yolander’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?
○ 24
○ 23
○ 22
○ 21
○ 19.5


When B started walking Y already has covered 3 miles out of 45, hence the distance at that time between them was 45-3=42 miles.

Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 42/7=6 hours. In 6 hours B walked 6*4=24 miles.

Answer: A.
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When bob starts walking The distance left between them is 45-3 = 42 miles

Time taken to meet = Distance / Relative speed
= 42/(3+4) = 6 hours

so, bob walked = 6 x 4 = 24 miles
Ans. A.
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New post 01 Dec 2011, 04:53
3+3t+4t=45
t=6
Bob==>4*6=24
==>A

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New post 24 Mar 2014, 04:11
Let say they meet after x hrs.

so 3x + 4 (x-1) = 45 "As Bob started after an hour"

after solving the above equation we get answer as 24

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Re: One hour after Yolanda started walking from X to Y, a distan [#permalink]

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New post 27 Mar 2014, 03:12
Yolanda has already covered 3 kms out of 45

So remaining distance = 42

Time taken by both to meet at a point will be the same in the stretch of 42 kms

Bob travels distance = x
Speed = 4

Yolaondu will travel = 42 - x
Speed = 3

\(\frac{x}{4} = \frac{42-x}{3}\)

x = 24 = Answer = A
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One hour after Yolanda started walking from X to Y, a distance of 45 m [#permalink]

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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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Re: One hour after Yolanda started walking from X to Y, a distance of 45 m [#permalink]

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Bunuel wrote:

GMAT weekly questions



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


Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 3(t + 1) miles. These distances must sum to 45 miles, so 4t + 3(t + 1) = 45, which may be solved for t as follows
4t + 3(t + 1) = 45
4t + 3t + 3 = 45
7t = 42
T = 6 (hours)
Therefore, Bob had walked 4t = 4(6) = 24 miles when they met. The best answer is A.
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This can be solved using the "Relative speed approach" as well. The advantage is that we can solve mentally.

Let's first talk about the concept of relative speed:

When two objects travel in the same direction, the relative speed of one with respect to another is the difference between the individual speeds.

And when two objects travel in the opposite direction, the relative speed is the sum of the individual speeds.

In this case, Yolanda’s<hereforth referred as Y> has a lead time of 1 hour. So distance already traveled by Y=3 miles.

Remaining distance to be covered when both Y and B move = 45-3=42.

This distance is covered at the net speed of \(3(Y's speed)+4(B's speed)= 7 mph (Opp direction)\)

So time taken by both to meet = \(\frac{42}{7} = 6\)

Distance traveled by B in 6 hours = \(6*4=24 miles\)
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Re: One hour after Yolanda started walking from X to Y, a distan [#permalink]

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New post 23 Oct 2014, 02:38
Since the speed of both are 3 and 4 , the end answer must be a multiple of both . Only 24 is present in that case.

This method might help in the worst case.
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Re: One hour after Yolanda started walking from X to Y, a distan [#permalink]

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New post 14 Apr 2016, 13:19
can someone tell me what I am missing please. I read the explanations, and still am not getting it. Why isn't it 12miles (i Know not an option)

Y=3 after 1st hour, 6 after 2 hours, 9 after 3 hours, 12 after 4 hours.
bob=4 after one, 8 after 2 ect

y has a 3 mile head start so..

y=3, B=0
y=6, b=4
y=9, B=8
y=12, b=12??

please explain. Thank you

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Re: One hour after Yolanda started walking from X to Y, a distan [#permalink]

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New post 15 Apr 2016, 02:08
ross14 wrote:
can someone tell me what I am missing please. I read the explanations, and still am not getting it. Why isn't it 12miles (i Know not an option)

Y=3 after 1st hour, 6 after 2 hours, 9 after 3 hours, 12 after 4 hours.
bob=4 after one, 8 after 2 ect

y has a 3 mile head start so..

y=3, B=0
y=6, b=4
y=9, B=8
y=12, b=12??

please explain. Thank you


The distance between X and Y is 45 miles so the combined distance covered also must be 45 miles.

y=3, B=0
y=6, b=4
y=9, B=8
y=12, b=12
y=15, b=16
y=18, b=20
y=21, b=24 --> 21 + 24 = 45.

Hope it's clear.
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One hour after Yolanda started walking from X to Y, a distan [#permalink]

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New post 30 May 2017, 17:33
kpadma 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 Bobт'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

1. In 1 hr Yolanda would have walked 3 miles
2. Yolanda and Bob both walk simultaneously after that and move towards each other.
3. They would have met after (45-3)/(3+4)= 6hrs
4. In 6 hrs, Bob would have walked , 6*4=24 miles
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