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

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A, B and C run around a circular track starting from the [#permalink] New post 28 Aug 2007, 18:29
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
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Re: Circular Race .. 700 level question [#permalink] New post 28 Aug 2007, 18:48
fresinha12 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
C
4 km = 4000 m
A makes it around the track 10 times in 1 hr, B 15 times and C 20 times.
in 60 minutes A will complete the track once every 6 (60/10) minutes, B once every 4 (60/15) minutes and C once every 3 (60/20) minutes.

6, 3 and 4's first common multiple is 12.
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Re: Circular Race .. 700 level question [#permalink] New post 28 Aug 2007, 18:56
fresinha12 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



I got C,

it will take 12 minutes for the runners to meet for the 1 st time.
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Re: Circular Race .. 700 level question [#permalink] New post 28 Aug 2007, 19:04
fresinha12 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


Well, I used backsolving and elimination for time consideration,

Since among ABC, A is the slowest runner, it will take at least

0,4/4 = 6 mins, so eliminate A and B

Start backsolving with C, 12 min=1/5 hours.

Multiply ABC speeds by the time, 1/5 hours, if the results are all multiples of 0,4 they do meet after this time at the starting point.

And since 12 min is the smallest value among left choices it must be the shortest time.
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 [#permalink] New post 28 Aug 2007, 19:10
A -> 4km/h
B -> 6km/h
C -> 8km/h

Length of track = 0.4km.

Test 12 mins, 12 mins = 0.2 hour. Distance A covers = 0.8km (2 laps), Distance B covers = 1.2km (3 laps), Distance C covers = 1.6 (4 laps).

Since A,B and C all cover full laps, they meet at the start point at 12 minutes.

(Whoops, got lucky here. Picked C and it worked)
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Re: Circular Race .. 700 level question [#permalink] New post 20 Jan 2008, 10:21
figure out how many minutes it will take either runner to make around the track. A = 6 min, B = 4 min, C = 3 min. Common multiple of these three is 12, So C should work.
Re: Circular Race .. 700 level question   [#permalink] 20 Jan 2008, 10:21
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