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

Question

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.

A. 3
B. 4.5
C. 4
D. 5.5
E. 5

KarishmaB · Accepted Answer

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) Check this video for when to use relative speed: https://youtu.be/wrYxeZ2WsEM

Blackbox · Answer

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 [ 11.96 KiB | Viewed 54216 times ]

tass · Answer

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

PareshGmat · Answer

Refer diagram below: speed.png 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

thorinoakenshield · Answer

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

KarishmaB · Answer

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.

ajdse22 · Answer

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.

NinetyFour · Answer

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.

AkshdeepS · Answer

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)

dave13 · Answer

VeritasKarishma how is it possible that B overtakes A in 2+6 = 8 hrs 8 hours B overtakes A in 6 hrs, it took only 6 hours to do the distance of 240 km for B to overtake A. While A did 60 km, B was not moving. So how can you attribute additional 2 hours to B ?

KarishmaB · Answer

The time is being calculated from "after A starts". Say A starts at 12 noon. 
B starts after 2 hrs so at 2 pm and then catches up with A after 6 hrs so at 8 pm.

So B overtakes A after '8 hrs' since the start of A at 12 noon. It doesn't matter whether he travelled at a constant rate in these 8 hrs or stopped and zoomed every half an hour.

IIIIIIIIIIIII · Answer

40*(t-2)=30*t This gets t=8 as the time when B is at the same point as A. 
60*(8-x)=30*8 This answers the question how many hours C is "allowed" to travel less than A to be at the point where A, B, (and C) meet. Solving this for x yields 4. (C)
I found this to be a very quick approach. However, if I just got the correct solution through luck, please tell as I just started to prepare.

prakashb2497 · Answer

Please let me know if my approach is correct?

Since the distance is travelled is constant, I assumed values and kept distance as 240.

Time for A is then 240/30 = 8 Hours.

Time for B is 240/40= 6+2

Time for K is 240/60 = 4+4.

I'm not sure if this approach is correct, please advise  KarishmaB  @bunnel

KarishmaB · Answer

My question is how did you get 240? 
If instead you had assumed 120 as the distance you would have got 120/30 = 4 hrs, 120/40 = 3 hrs so B would have started 1 hour after A. This means that actually the distance covered is twice i.e. 240. Then you can use 240 to get the time taken by K.

saynchalk · Answer

In 2 hours, A travels 60 KM

60/(40-30) = 6 hours

For K to cross 60 KM relative to A = 60/(60-30) = 2 hours

B started 2 hours later, so 6+2 = 8 hours taken, and similarly, K took 2+2 = 4 hours

chetan2u   Bunuel , I know I'm missing something but I can't put my finger on it, can you help me to refine this so it's foolproof?

chetan2u · Answer

How did you get '
B started 2 hours later, so 6+2 = 8 hours taken, and similarly, K took 2+2 = 4 hours'..
Why should k start 2 hours after A ??

saynchalk · Answer

I used the relative speed formula for B, and it is mentioned that he started 2 hours later so I added a 2 to the answer since he will take 2 hours more than what it would normally with his relative speed Then I used the relative speed formula for K, and added 2 since 2 hours wasn't in the answers so I figured I had messed up somewhere

bumpbot · Answer

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