
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 4th, 2018, 03:01 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 470 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: somewhere Posts: 636 Thanks: 91 
$\displaystyle T=lcm(v_A , v_B ) = lcm(7,5)=35$ 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: 14,597 Thanks: 1038 
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? 
October 4th, 2018, 10:30 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  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 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219  
October 4th, 2018, 11:52 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
October 4th, 2018, 07:59 PM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 470 Thanks: 1  
October 4th, 2018, 11:26 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
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 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  

Tags 
answer, match, method 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
good/bad of simplex method and big M method  carlluis  Linear Algebra  1  April 5th, 2018 10:49 AM 
Method's name  Zap  Elementary Math  1  October 7th, 2014 07:54 AM 
LP with BigM Method  waytogo  Applied Math  0  May 23rd, 2012 12:28 AM 
My Method  MichaelTannock  New Users  0  May 5th, 2012 11:01 AM 
What is the method?  guru123  Algebra  2  December 31st, 1969 04:00 PM 