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A, B, K start from the same place and travel in the same direction at
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07 Dec 2014, 04:36
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45% (medium)
Question Stats:
70% (02:33) correct 30% (02:53) wrong based on 202 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?
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10 Dec 2014, 23:58
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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
Please include your explanation.
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.
Answer (C)
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A, B, K start from the same place and travel in the same direction at
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07 Dec 2014, 07:53
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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 https://www.youtube.com/watch?v=Wqu1xKudqJQ
So, to solve this question, set up a table like this
Re: A, B, K start from the same place and travel in the same direction at
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07 Dec 2014, 05:47
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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
Re: A, B, K start from the same place and travel in the same direction at
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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 https://www.youtube.com/watch?v=Wqu1xKudqJQ
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.
_________________
Re: A, B, K start from the same place and travel in the same direction at
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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
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Re: A, B, K start from the same place and travel in the same direction at
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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?
Re: A, B, K start from the same place and travel in the same direction at
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20 Jan 2015, 22:43
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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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Re: A, B, K start from the same place and travel in the same direction at
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06 Jul 2016, 00:30
1
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.
Re: A, B, K start from the same place and travel in the same direction at
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20 Jan 2019, 14:34
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
Please include your explanation.
My thought process if it helps anyone:
B and K overtake A at the same instant, this little phrase tells us everything we need to solve the question. This means that the distance traveled by A, B, and K are equal.
Let's say A travels for T hours. B started 2 hours after A, so that means B travels for T-2 hours.
Hence:
distance traveled by A = distance traveled by B
30t = 40(t-2) t = 8
Total distance traveled by A, B and K = 240 kilometers. It takes K 4 hours to travel 240 km, hence K started 4 hours after A.
Re: A, B, K start from the same place and travel in the same direction at
[#permalink]
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05 Mar 2019, 09:51
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 https://www.youtube.com/watch?v=Wqu1xKudqJQ
So, to solve this question, set up a table like this
Re: A, B, K start from the same place and travel in the same direction at
[#permalink]
Show Tags
05 Mar 2019, 10:19
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
Please include your explanation.
Rate of A = 30 km/hr
Let time of A = T hours
Rate of B = 40 km/hr
As per question, time of B = Time of A - 2 = T - 2 hours
Rate of K = 60 km/hr
Important : When two objects move from the same place in same direction and one object overtakes the other, they travel equal distance.
So, Distance travelled by A = Distance travelled by B (When B overtakes A)
30T = 40 (T - 2)
30 T = 40T - 80
T = 8
Now, Distance travelled by A = 30 * 8 = 240 kms
Distance travelled by B = 40 * 8 - 80 = 240 kms
Now question says B and K overtake A at the same time, means B and K have travelled the same distance,
Therefore, Distance travelled by K = 240 kms
Speed of K * Time of K = 240
60 * Time of K = 240
Time of K = 4 hours
Difference of time between A's and K's = 8 - 4
4 hours (C)
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70% (02:33) correct 
I chose A because after getting 6h ( to over take A), I forgot to add the extra 2h, stupid mistake 
