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-   -   Why first method answer didn't match second method? (http://mymathforum.com/algebra/345070-why-first-method-answer-didnt-match-second-method.html)

Ganesh Ujwal October 4th, 2018 03:01 AM

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.

idontknow October 4th, 2018 04:03 AM

$\displaystyle T=lcm(v_A , v_B ) = lcm(7,5)=35$
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 $\displaystyle lcm(t_1,t_2)$

Denis October 4th, 2018 10:01 AM

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?

Ganesh Ujwal October 4th, 2018 10:30 AM

Quote:

Originally Posted by Denis (Post 600395)
The time t it takes for 1st meeting to occur is d / (b - a),

Can I use this formula for all circular track problems?

skipjack October 4th, 2018 10:43 AM

Quote:

Originally Posted by Ganesh Ujwal (Post 600370)
(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.

Denis October 4th, 2018 11:52 AM

Quote:

Originally Posted by Ganesh Ujwal (Post 600402)
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

Ganesh Ujwal October 4th, 2018 07:59 PM

Quote:

Originally Posted by Denis (Post 600395)
at + d = bt
bt - at = d
t(b - a) = d
t = d / (b - a)

Why did you wrote this 4 equations in the solution?

skipjack October 4th, 2018 11:26 PM

They're just the steps that can be used to solve for t, given the first equation and that b doesn't equal a.

Denis October 5th, 2018 05:36 AM

Quote:

Originally Posted by Ganesh Ujwal (Post 600463)
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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