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

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

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New post 07 Dec 2014, 04:36
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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

Please include your explanation.
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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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New post 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  [#permalink]

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New post 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
Attachment:
Untitled.png
Untitled.png [ 11.96 KiB | Viewed 8422 times ]
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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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New post 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
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A, B, K start from the same place and travel in the same direction at  [#permalink]

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New post 07 Dec 2014, 05:51
Could you please care to explain the equations?
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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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New post 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.
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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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New post 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?
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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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New post 07 Dec 2014, 08:17
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A, B, K start from the same place and travel in the same direction at  [#permalink]

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New post 10 Dec 2014, 22:12
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Refer diagram below:

Attachment:
speed.png
speed.png [ 4.57 KiB | Viewed 8239 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

Answer = C
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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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New post 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 :(
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New post 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  [#permalink]

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New post 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
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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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New post 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.
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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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New post 06 Jul 2016, 00:30
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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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New post 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.
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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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New post 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
Attachment:
Untitled.png


can you please explain how you got the 240km?
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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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New post 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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Re: A, B, K start from the same place and travel in the same direction at   [#permalink] 05 Mar 2019, 10:19
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