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 October 4th, 2018, 03:01 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 343 Thanks: 1 Why first method answer didn't match second method? On a circular track of length 100m. A and B start running clockwise from the same point with speeds of 5m/sec and 7m/sec respectively. After how much time will they meet for the first time while running? First method: Track = 100m → SA/SB = 5/7 A does 5 rounds B does 7 rounds Difference = 2; It's their second meeting. B overtakes A somewhere in the middle 5/7 Written as 2.5/3.5 A does 2.5 rounds, B does 3.5 rounds. Then difference is 1. It means faster guy “B” overtakes “A” for first time. If 2 meetings happened → 100 sec → (5*20) A → 20 sec When would they first meeting would happened. → 100/2 = 50 sec Second method: (Total distance)/(Relative distance) = 100/(7 - 4) = 100/3 sec After 100/3 sec, A and B meet for first time. Last edited by skipjack; October 4th, 2018 at 10:41 AM.
 October 4th, 2018, 04:03 AM #2 Senior Member   Joined: Dec 2015 From: iPhone Posts: 480 Thanks: 73 $\displaystyle T=lcm(v_A , v_B ) = lcm(7,5)=35$ I write a formula below : If A does a round for time $\displaystyle t_1$ If B does a round for time $\displaystyle t_2$ then they meet again at the same point after time $\displaystyle lcm(t_1,t_2)$ Last edited by idontknow; October 4th, 2018 at 04:06 AM.
 October 4th, 2018, 10:01 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,316 Thanks: 1023 The time t it takes for 1st meeting to occur is d / (b - a), where d = track length (100), b = faster speed (7), a = slower speed (5) at + d = bt bt - at = d t(b - a) = d t = d / (b - a) So: t = 100 / (7 - 5) = 50 WHY are you trying your obscure 2nd calculation? Thanks from Ganesh Ujwal
October 4th, 2018, 10:30 AM   #4
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Quote:
 Originally Posted by Denis The time t it takes for 1st meeting to occur is d / (b - a),
Can I use this formula for all circular track problems?

Last edited by skipjack; October 4th, 2018 at 10:39 AM.

October 4th, 2018, 10:43 AM   #5
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Quote:
 Originally Posted by Ganesh Ujwal (Total distance)/(Relative distance) = 100/(7 - 4) = 100/3 sec
Why did you give "100/(7 - 4)" instead of "100/(7 - 5)", which gives 50 seconds, as expected.

October 4th, 2018, 11:52 AM   #6
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Quote:
 Originally Posted by Ganesh Ujwal Can I use this formula for all circular track problems?
Yes, for all SIMILAR problems.
The other 3 variables (a, b and d) are easily derived:
d = t(b - a)
a = (bt - d) / t
b = (d + at) / t

October 4th, 2018, 07:59 PM   #7
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Quote:
 Originally Posted by Denis at + d = bt bt - at = d t(b - a) = d t = d / (b - a)
Why did you wrote this 4 equations in the solution?

 October 4th, 2018, 11:26 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,472 Thanks: 2039 They're just the steps that can be used to solve for t, given the first equation and that b doesn't equal a.
October 5th, 2018, 05:36 AM   #9
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Quote:
 Originally Posted by Ganesh Ujwal Why did you wrote this 4 equations in the solution?
C'mon Ganesh, that's a silly question: are you joking?

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