One hour after Matthew started waking from x to y, a distanc

Question

One hour after Matthew started waking from x to y, a distance of 45km, Johnny started walking along the same road from y to x. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny 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

MacFauz · Accepted Answer

Just an alternative method...

After the first hour the distance is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.

Hence A.

Marcab · Answer

The best method to solve such questions is the summation of distance method.
Please note that when Matthew and Johny would meet, the sum of the distance covered will be the lenth of the journey i.e. 45 km.
Distance covered by Matthew= 3(t+1) 
Distance covered by Johny= 4t 
where t=time taken by Johny.
Therefore  3(t+1) + 4t = 45 
t will come as 6.
Distance covered by Johny is  4t  or  4*6 = 24km  Ans.
+1A

chiccufrazer1 · Answer

wow..u have done in a simple way indeed..i tried using the train's formula which states that (v2+v1)*t=D,but it did not work..would you please explain to me why i had problems using that formula?

Posted from my mobile device

Marcab · Answer

I assume that v1 and v2 are respective speeds.
Here the formula won't work because the two start at different times. Had they started at same time, the formula would have been justified.
I hope you getting my point.

chiccufrazer1 · Answer

what would happen if the were walking in the same direction?

Posted from my mobile device

MacFauz · Answer

In such a case, the total distance would be irrelevant.

In the 1st hour Mathew would have travelled 3 kms. 
Let us say that after this first hour it takes Matthew and Johnny "t" hours to meet.
So, distance travelled by Matthew and distance travelled by Johnny should be the same.

Distance travelled by Matthew = 3 + 3*t
Distance travelled by Johnny = 4*t

3 + 3*t = 4*t. So, t = 3 hrs. So distance travelled would be = 4*3 = 12 kms

bhavinshah5685 · Answer

I used the train formula but modified the distance travelled.

After one hour, mathew has travelled 3 kms so 42 kms left when Johnny starts.

so distance to travel is 42 kms for both, in bwtween which they will meet,

No d = 42 kms
t = hrs
speed = 3+4 (since they moving in opposite direction to each other) = 7

s = d/t
7 = 42/t
t = 6 hrs

So distance travelled by John = 4*6 = 24 kms

Option A

Triforce · Answer

Since M started walking one hour before J the distance they have to travel together has to be 45km-3km/h*1h=42km

The combinded speed of M and J is 3km/h+4km/h=7km/h. They thus need 42km/7(km/h)=6h to cover the 42km between them. Therefore J has to walk 4km/h*6h=24km

sambam · Answer

If Matthew has an hour heads start then that means the distance between them when Johnny starts walking is 42kms. Each hr their combined distance travelled is 7 kms (3km/hr + 4km/hr). That must mean that it will take 6 hours for them to meet each other.

In 6 hrs Johnny walked 6x4 = 24 kms.
Answer: A

In 6 hrs Johnny walked 6x4 = 24 kms.
Answer: A

chiccufrazer1 · Answer

can we approach this problem in the same way(willard types at an average speed of 40 words per minute and george types at 60 words per minute.if willard begins typing a manuscript at 4:20 and george begins typing an identical copy of the manuscript at 5:00,at what time will they be typing the same word? 
A.5:10 B.5:30 C.5:40 D.6:00 E.6:20''

Posted from my mobile device

Perhaps · Answer

speed of mathew = 3 kph
let time be 't'
tot dist travelled by mathew = 3t

johny starts an hour later ...so john's time would be = t-1
speed of johny = 4 kph
tot dist travelled bby johny = 4(t-1)

since tot dist given is 45 kms so...
3t + 4(t-1) = 45
7t - 4 = 45
7t = 41
t= 41/7 hrs

so tot dist travelled by johny is = 4(t-1)
 = 4 ( 41/7 - 1)
= 4 ( 34/7)
= 136/7
= 19.42 = 19.5 (approx0

so answer is E.

if its wrong...please explain me the reason...

Bunuel · Answer

The red part above is not correct: 7t - 4 = 45 --> 7t = 49 --> t = 7 --> 4(t - 1) = 24.

Hope it helps.

Perhaps · Answer

oops...

thanks bunuel

gvvsnraju@1 · Answer

By the time Jhonny Started, Mathew had already traveled 3 KM.
So the distance left between jho & Mat is 42 km.
Relative Speed = 3 + 4 = 7 km as both are moving towards each other.
So Both will meet after 42/7 = 6 hours.
So Math travels = 4 * 6 =24 Km

Regards
G V V S Narayana raju

Nunuboy1994 · Answer

3(x+1) + 4(x) =45
 3x + 3 +4x =45
 7x =42
 x= 6

4(6)= 24

A

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

One hour after Matthew started waking from x to y, a distanc

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

One hour after Matthew started waking from x to y, a distanc

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards