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: https://i.imgur.com/NlPZkA6.jpg 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. 
$\displaystyle T=lcm(v_A , v_B ) = lcm(7,5)=35$ 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 $\displaystyle lcm(t_1,t_2)$ 
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? 
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The other 3 variables (a, b and d) are easily derived: d = t(b  a) a = (bt  d) / t b = (d + at) / t 
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They're just the steps that can be used to solve for t, given the first equation and that b doesn't equal a. 
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