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

Question

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

(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.

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.

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

APPROACH #1:   
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

APPROACH #2:  
For this approach let's start with a word equation. 
Since Yolanda's is 1 hour longer than Bob's travel time we can write:   Yolanda's travel time  =  Bob's travel time  + 1

Let  d  = the distance Bob had walked when they met
So,  45 - d  = the distance Yolanda had walked when they met (since the two people travel a total of 45 miles)

Time = distance/rate , so we can plug the following values into our word equation: 
  (45 - d)/3  =  d/4  + 1  
Multiply both sides of the equation by 12 to get:  180 - 4d = 3d + 12 
Add 4d to both sides of the equation:  180 = 7d + 12 
Subtract 12 from both sides of the equation:  168 = 7d 
Solve:  d = 168/7 = 24 
Answer: A

anandnk · Answer

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.

MHIKER · Answer

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.

panksgmat · Answer

3+3t+4t=45
t=6
Bob==>4*6=24
==>A

Ravithj · Answer

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

PareshGmat · Answer

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

Bunuel · Answer

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.

samirchaudhary · Answer

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, Yolandaâ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

prashd · Answer

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.

ross14 · Answer

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

Bunuel · Answer

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.

SVaidyaraman · Answer

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

hemantbafna · Answer

Distance=45 miles

Yolanda's speed=3 miles/hr Bob's speed=4 miles/hr

Distance between them when Bob starts=42 (as Yolanda has covered a distance of 3 miles)

The time they will meet = 42/(3+4) miles/hr=6 hr

Miles Bob walked when they met= 4 miles/hr *6 hr=24 miles

A

CrackverbalGMAT · Answer

Yolanda has already covered 3 miles in one hour.

Out of 45miles, distance left to cover = 45-3 =42 miles

The relative speed = 3+4=7 miles/hr

Time to cover it = 42/7 =6 hour.

In 6 hours, B @4mph would have walked 6 * 4 = 24miles.

(option a)

D.S
GMAT SME

Crytiocanalyst · Answer

let be the time taken x be the distance from X

t=x/3 , t-1 = 45-x/4 
=>x/3+x-45/4 = 1
=>x=21

we want from Y 45-21 = 24 
therefore IMO A

gmatchile1 · Answer

Welcome to the challenging and exciting world of GMAT Focus Edition. I'm Claudio Hurtado, your expert guide to GMAT Focus Edition in the Quantitative Reasoning section, here to take you through a journey full of discoveries and problem solving.
Imagine this scene: Yolanda embarks on a journey from point X to Y, while Bob begins his walk in the opposite direction, from Y to X, an hour later. The distance between them covers 45 miles. Yolanda walks at a steady pace of 3 miles per hour, while Bob walks at a brisk pace of 4 miles per hour. The question that arises is: how many miles had Bob walked when they finally met?

This is the time to apply our problem-solving skills. We must carefully analyze the situation and develop a strategy to discover the answer.

Let's see it step by step. Suppose t represents the number of hours Bob had walked when he met Yolanda. At that time, Bob had traveled 4t miles, while Yolanda, having walked for an hour more, had traveled 3(t + 1) miles. Together, their distances should add up to a total distance of 45 miles.
Now, armed with this equation, we embark on our search for the solution:

4t + 3(t + 1) = 45

Expanding and simplifying, we find:

7t + 3 = 45

7t = 42

Solving for t, we find that t is equal to 6 hours. Therefore, when they met, Bob had traveled 4t miles, which is equivalent to 4 multiplied by 6, resulting in 24 miles.

Confidently, we concluded that Bob had walked 24 miles when they crossed paths. The right answer? A resounding option A.

This problem serves as a testament to the power of analytical thinking and strategic problem-solving techniques. With Claudio Hurtado (+56 945 517 215) as your trusted guide, you'll navigate the complexities of the GMAT Focus Edition with ease, unlocking doors to success, one problem at a time.
So, equip yourself with determination and embark on this exciting journey with me. Together, we will conquer the Quantitative Reasoning section of the GMAT Focus Edition and emerge victorious.

Claudio Hurtado, classes, courses and leveling of GMAT Focus Edition competencies in Quantitative Reasoning section. Book your classes today,  clasesgmatchile@gmail.com  , +56 945 517 215,  gmatchile.cl ,  clasesgmat.es

hemanthPA · Answer

Visulaize

In 1hr Y would have travlled 3 miles, so the relative distance between them would be reduced from 45 miles to 42 miles,

Relative speed between the both after the first hour and when B starts would be = 4+3 = 7

T = Rd/Rs = 42m/7mph = 6h

Now in 6hrs @ 4mph B would travel 24m

bumpbot · Answer

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