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Time n Distance Problem
by sakthi mithun - Wednesday, 19 October 2011, 12:14 PM
  A starts from a point P on a circular track ,at 6:00 am and runs around the track in clockwise direction .At 6:15 am ,B starts from the same point P and runs around the track in counter clockwise direction and meets A for the first time at 7:09 am.If B started at 6 am then he would have met A for the first time at 7 am.If both A & B start from P at 7:00 am and run in the opposite direction,then find the time at which they would meet at the starting point for the first time?
Re: Time n Distance Problem
by TG Team - Wednesday, 19 October 2011, 01:50 PM
 

12:00 noon. smile

Kamal Lohia

Re: Time n Distance Problem
by Aditya Wagholikar - Sunday, 30 October 2011, 07:01 PM
  PLEASE EXPLAIN THE METHOD
Re: Time n Distance Problem
by nisarg thakkar - Sunday, 13 November 2011, 10:41 PM
  dear sakthi,
can u xplain d method please! smile
Re: Time n Distance Problem
by TG Team - Monday, 14 November 2011, 04:07 PM
 

Let's say 'a' unit/min and 'b' unit/min be the speeds of A and B respectively.

Equating total distance around the circle from given two conditions we get:

69a + 54b = 60a + 60b

=> 9a = 6b or a:b ≡ 2:3

So they will be meeting at same starting point for the first time in their 5th meeting. And they are meeting for the first time after 1hr of starting. Thus the required time is 12 noon. smile

Kamal Lohia  

Re: Time n Distance Problem
by Brejesh Kumar Gupta - Tuesday, 26 March 2013, 05:39 PM
  8:03 A.M.

Re: Time n Distance Problem
by Ramesh gayakwad - Sunday, 16 June 2013, 09:55 AM
 

Sir,

a:b = 2:3

then how they will meet at the same starting point in their 5th meeting comes?

Is it (2+3)= 5????

Pls explain so that we can have a generalised form of it..

Re: Time n Distance Problem
by Fareed Un - Thursday, 12 September 2013, 11:18 PM
  I would start solving the question from the beginning.

Step # 01:
'Find the ratio of the speed of A and B'
The distance which B alone covered in 15 minutes, is covered in 9 minutes when A and B start to travel together.

B = 15 minutes
A + B = 9 minutes

A:B = 2:3

(We assume that the speed of A and B is 2 kph and 3 kph respectively)

Step # 02
'Find the total circumference of the circle'
If A traveled @ 2 kph and B traveled @ 3 kph for 69 min and 54 min respectively, then the total distance covered by:
A = 2 * 69 / 60 = 2.3 km
B = 3 * 54 / 60 = 2.7 km

Circumference = 5 km

Step # 03
'Finding the time when A and B are at starting point'
For A
It would take 2.5 hours to complete one rotation of the circle.
2.5 hrs = 1 rotation
5 hrs = 2 rotations
7.5 hrs = 3 rotations
10 hrs = 4 rotations
12.5 hrs = 5 rotations
15 hrs = 6 rotations

For B
It would take 1.6667 hours to complete one rotation of the circle.
1.6667 hrs = 1 rotation
3.3333 hrs = 2 rotations
5         hrs = 3 rotations
8.3333 hrs = 4 rotations
10       hrs = 5 rotations

Step # 04
'Finding the ultimate point'
It is noteworthy that after 10 hrs, A has completed 4 rotations and B has completed 5 rotations.

it means that after 10 hrs of the start, both A and B would meet at the starting point for the first time.


So the correct answer is 7:00 am + 10 hrs = 5:00 pm

Re: Time n Distance Problem
by Fareed Un - Thursday, 12 September 2013, 11:23 PM
  I think I have answered the question correctly, but it took around 45 min for me to fully understand and solve the question.

Please give me a generalized formula that can be applied to the scenarios like the one in the question, so that we can save time.

thanx