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# A, B and C run around a circular track starting from the

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Director
Joined: 26 Sep 2005
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Location: Munich,Germany
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A, B and C run around a circular track starting from the [#permalink]  02 Mar 2006, 03:14
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A, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?

1 minute
5 minutes
12 minutes
20 minutes
24 minutes
Intern
Joined: 17 Feb 2006
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Re: PS: Races [#permalink]  02 Mar 2006, 07:39
shahnandan wrote:
A, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?

1 minute
5 minutes
12 minutes
20 minutes
24 minutes

Since we need the starting point, we need to figure out how often they get to the starting point:
A = 4 km/h / 400 m = 10 times/h = every 6 minutes
B = 6 km/h / 400 m = 15 times/h = every 4 minutes
C = 8 km/h / 400 m = 20 times/h = every 3 minutes

We need to find the GCD, which is 2^2*3 = 12, so the cars will meet after 12 minutes at the starting point of the track.

Manager
Joined: 04 Sep 2005
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Location: Fringes of the Boreal, Canada
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First figure out meters per minute

M = meters

Runner A: 4 km/h = 4000 M/h = 4000/60 M/min ; 400/4000/60 = 6 min to run the 400 meter track

Runner B: 6km/h = 6000M/h = 100 M/h; 400/100 = 4min

Runner C: 8km/h .. .... ; 3min to run the 400 meter track

They will all meet at the starting point at the 12 minute mark.
_________________

"To hell with circumstances; I create opportunities." - Bruce Lee

Manager
Joined: 04 Sep 2005
Posts: 142
Location: Fringes of the Boreal, Canada
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: PS: Races [#permalink]  02 Mar 2006, 07:44
gpmagnus wrote:
shahnandan wrote:
A, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?

1 minute
5 minutes
12 minutes
20 minutes
24 minutes

Since we need the starting point, we need to figure out how often they get to the starting point:
A = 4 km/h / 400 m = 10 times/h = every 6 minutes
B = 6 km/h / 400 m = 15 times/h = every 4 minutes
C = 8 km/h / 400 m = 20 times/h = every 3 minutes

We need to find the GCD, which is 2^2*3 = 12, so the cars will meet after 12 minutes at the starting point of the track.

ahh, you beat me to it!
_________________

"To hell with circumstances; I create opportunities." - Bruce Lee

Manager
Joined: 20 Feb 2006
Posts: 213
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Good problem dude! I applied a long method with no answer finally !!
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