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Three friends-whose walking rates are .....

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Three friends-whose walking rates are ..... [#permalink] New post 05 Oct 2010, 04:41
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Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference.After how many minutes are the three of them together again?

A. 5 mins
B. 10 mins
C. 15 mins
D. 3 mins
E. 7 mins
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Re: Three friends-whose walking rates are ..... [#permalink] New post 05 Oct 2010, 05:13
Answer will be A. Whats the OA?

The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 5mins.

Maybe someone can show this with a better explanation.
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Re: Three friends-whose walking rates are ..... [#permalink] New post 05 Oct 2010, 06:21
i got A as the answer. i set it up as follows

if A = 1ft/sec then with a distance of 300 ft, it would take A 300 seconds to complete
if B = 3ft/sec then with a distance of 300 ft, it would take B 100 seconds to complete
if C = 6ft/sec then with a distance of 300 ft, it would take C 50 seconds to complete

we can find the amount of time it would take for them to meet again by taking the LCM of the each of their times

the LCM of 300, 100, and 50 is 300. so 300 seconds converted to minutes is 5 minutes.

was this the OA?
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Re: Three friends-whose walking rates are ..... [#permalink] New post 05 Oct 2010, 11:32
pzazz12 wrote:
Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference.After how many minutes are the three of them together again?

A. 5 mins
B. 10 mins
C. 15 mins
D. 3 mins
E. 7 mins


Nice question !

To make this easier, you can assume that person 1 is standing still at the starting point and persons2 and 3 are moving at 2ft/sec and 5ft/sec
To satisfy the criterion of all three meeting, they would have to meet back at the start.
Person 2, does a circle every 300/2=150sec
So he will be at the start on these times {150,300,450,...}
Person 3 does the circle in 300/5=60sec
So he will be at the start at these times {60,120,180,240,300,....}

The least common time is 300sec or 5min

Answer is (A)
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Re: Three friends-whose walking rates are .....   [#permalink] 05 Oct 2010, 11:32
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