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# Three friends

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Joined: 10 Nov 2004
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28 Nov 2004, 11:33
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Three friends A, B and C run around a circular track of length 120 metres at speeds of 5 m/s, 7 m/sec and 15 m/sec, starting simultaneously from the same point and in the same direction. How often will the three of them meet?

(1) Every 60 seconds (2) Every 120 seconds
(3) Every 30 seconds (4) None of these

Manager
Joined: 13 Oct 2004
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28 Nov 2004, 18:40
Backsolved here, but not clear on the algebraic approach apart from knowing that you need to use distance mod 120.
Manager
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28 Nov 2004, 18:42
Revital,
Thanks.
Intern
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29 Nov 2004, 08:21
ok will do it for next time
sorry
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29 Nov 2004, 08:44

this problem can be solved using relative speed.
take two people at a time first take A and B. their relative speed is 7-5=2 m/s
the time that they will meet is 120/2= 60 seconds
now take.. B and c . their relative speed is 15-7=8m/s
the time that they will meet is 120/8= 15 seconds

now take common multiples of 15 and 60 ..which will be 60,120 etc..
the other way to look at it is.. take LCM of 15 and 60.. which would be 60.. so they will meet every 60 seconds.
29 Nov 2004, 08:44
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