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# A, B, K start from the same place and travel in the same direction at

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Manager
Joined: 30 May 2012
Posts: 210
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 04:36
1
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Difficulty:

45% (medium)

Question Stats:

71% (01:55) correct 29% (02:09) wrong based on 194 sessions

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A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?

A) 3
B) 4.5
C) 4
d) 5.5
e) 5

Manager
Joined: 30 May 2012
Posts: 210
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 07:53
5
4
Mods - I don't know if I am allowed to provide a link to a youtube video explaining a distance/speed concept. If I am not, please let me know and I will delete my post.

I found a neat explanation of a concept that can be used to solve the type of question I posted earlier. For those interested, here it is

So, to solve this question, set up a table like this
Attachment:

Untitled.png [ 11.96 KiB | Viewed 5016 times ]
##### General Discussion
Intern
Joined: 16 Apr 2013
Posts: 2
Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 05:47
1
B and K overtake in the same instant. So B overtake in (2*30)/(40-30) = 6 hours. That means B met after A went 8 hours.
So K starts after 30*8/60 = 4 hours
Manager
Joined: 30 May 2012
Posts: 210
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 05:51
Could you please care to explain the equations?
Math Expert
Joined: 02 Sep 2009
Posts: 47946
Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 07:57
Blackbox wrote:
Mods - I don't know if I am allowed to provide a link to a youtube video explaining a distance/speed concept. If I am not, please let me know and I will delete my post.

I found a neat explanation of a concept that can be used to solve the type of question I posted earlier. For those interested, here it is

So, to solve this question, set up a table like this

Attachment:
table.jpg

You are most welcome to post any relevant links.

P.S. Image in your post does not show up.
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Manager
Joined: 30 May 2012
Posts: 210
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 08:17
There was a typo in the screen grab earlier, so I took it down and posted a new one. Does the new one still doesn't show?
Math Expert
Joined: 02 Sep 2009
Posts: 47946
Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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07 Dec 2014, 08:17
Blackbox wrote:
There was a typo in the screen grab earlier, so I took it down and posted a new one. Does the new one still doesn't show?

It's fine now. Thank you!
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Posts: 1835
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Concentration: General Management, Technology
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A, B, K start from the same place and travel in the same direction at  [#permalink]

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10 Dec 2014, 22:12
3
1
Refer diagram below:

Attachment:

speed.png [ 4.57 KiB | Viewed 4866 times ]

Speed of A = 30 km/hr

Speed of B = 40 km/hr

Stage I

B starts 2 hours after A, means that A has already travelled 60 Kms when B kicked off

Stage II

Say A further travels distance "x" where all 3 meet

Time taken by A to travel distance "x" = Time taken by B to travel distance "60+x"

$$\frac{x}{30} = \frac{60+x}{40}$$

4x = 3x + 180

x = 180

Total catch point distance = 60+180 = 240

Time required by A from start $$= \frac{240}{30} = 8 Hrs$$

Time required by K from start $$= \frac{240}{60} = 4 Hrs$$

Time difference between A & K = 8-4 = 4Hrs

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Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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10 Dec 2014, 23:58
2
1
Blackbox wrote:
A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?

A) 3
B) 4.5
C) 4
d) 5.5
e) 5

You can use relative speed concepts here:
B starts 2 hrs after A so A covers 30*2 = 60 km in that time while B is still at starting point.

B makes up 10 km of relative distance every hour because the difference in their speed is 10 km/hr so it takes 60/10 = 6 hrs to cover additional 60 kms and overtake A. So B overtakes A in a total of 2+6 = 8 hrs since A started.

A will be 30*8 = 240 kms away from the starting point at this time. This is also the point where K overtakes A.
K will cover this distance in 240/60 = 4 hrs. So K must have started 8-4 = 4 hrs after A.

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Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Intern Joined: 25 Jun 2014 Posts: 39 Re: A, B, K start from the same place and travel in the same direction at [#permalink] ### Show Tags 11 Dec 2014, 00:45 I chose A because after getting 6h ( to over take A), I forgot to add the extra 2h, stupid mistake Senior Manager Joined: 02 Dec 2014 Posts: 382 Location: Russian Federation Concentration: General Management, Economics GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications) Re: A, B, K start from the same place and travel in the same direction at [#permalink] ### Show Tags 17 Dec 2014, 05:51 After 2 hours A travels (t+2)30 km. When B catches up their distances are equal. Hence (t+2)30=40t ==> t=6. Now K is traveling 60 km and B is at 40 km. K needs (60/40) time less to catch up A. Hence K needs (6/(3/2))=4 hours. Hope it helps _________________ "Are you gangsters?" - "No we are Russians!" Manager Joined: 03 Jan 2015 Posts: 65 Concentration: Strategy, Marketing WE: Research (Pharmaceuticals and Biotech) Re: A, B, K start from the same place and travel in the same direction at [#permalink] ### Show Tags 20 Jan 2015, 20:40 Hi all, I need some help in understanding this problem. As you can see my answer comes close to 4 and in exam I would correctly "guess" ANSWER C and move on. But I am not understanding the rationale behind solution properly. Following is how I see it and I am stuck in this method of solving it. Can someone please help me? TO Attachments Problem.jpg [ 44.83 KiB | Viewed 4560 times ] Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8187 Location: Pune, India Re: A, B, K start from the same place and travel in the same direction at [#permalink] ### Show Tags 20 Jan 2015, 22:43 thorinoakenshield wrote: Hi all, I need some help in understanding this problem. As you can see my answer comes close to 4 and in exam I would correctly "guess" ANSWER C and move on. But I am not understanding the rationale behind solution properly. Following is how I see it and I am stuck in this method of solving it. Can someone please help me? TO The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same. We know their rates are 30, 40 and 60. Say the time taken by B is T hrs. Then A takes 2+T hrs. And we need to find the time taken by K. Distance covered by A = Distance covered by B 30*(2+T) = 40*T T = 6 hrs Distance covered by B = Distance covered by K 40*T = 60*Time taken by K Time taken by K = 40*6/60 = 4 hrs Time taken by A = 2+T = 2+6 = 8 hrs Time taken by K = 4 hrs So K starts 8-4 = 4 hrs after A. _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
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Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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06 Jul 2016, 00:30
One way to solve this problem.
A set off 2 hours prior to B. This implies A is 60 km ahead of B. So B will take 60/(40-30) hours=> 6 hours. Now B has travelled 6*40 = 240 kms. A can do 240 in 8. To do 240, K needs only 4 hours however. So K must have left 8-4 = 4 hours after A left.
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Re: A, B, K start from the same place and travel in the same direction at  [#permalink]

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08 Dec 2017, 13:27
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