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# Two people are walking around a circular track. They start at 8 A.M.

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Senior Manager
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Joined: 23 Apr 2019
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Two people are walking around a circular track. They start at 8 A.M.  [#permalink]

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17 Sep 2019, 11:28
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00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:04) correct 33% (01:49) wrong based on 29 sessions

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Two people are walking around a circular track. They start at 8 A.M. from the same point but travel in opposite directions. The first person walks at a speed of two rounds per hour and the second person walks at a speed of three rounds per hour. How many times will they cross each other before the clock shows 9:30 A.M.?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
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Joined: 29 Jun 2019
Posts: 467
Re: Two people are walking around a circular track. They start at 8 A.M.  [#permalink]

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17 Sep 2019, 11:45
First person's speed is 1/30
and second one's is 1/20.
So, (1/20 + 1/30)×X =1
5/60*x=1
X=60/5=12
That is they meet each other first time, after 12 minutes.
9:30-8=1:30 or 90 minutes
90÷12=~7
Option C

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Two people are walking around a circular track. They start at 8 A.M.  [#permalink]

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17 Sep 2019, 17:25
Assume the perimeter of the track=x

Speed of first person= $$\frac{2*x}{1}$$=2x
Speed of second person= $$\frac{3*x}{1}$$=3x

Time taken by them to meet first time=$$\frac{x}{(2x+3x)}$$=$$\frac{1}{5}$$ hrs= 12 minutes

Number of times they cross each other before 9:30AM= [$$\frac{1.5*60}{12}$$]=[7.5]=7

Hovkial wrote:
Two people are walking around a circular track. They start at 8 A.M. from the same point but travel in opposite directions. The first person walks at a speed of two rounds per hour and the second person walks at a speed of three rounds per hour. How many times will they cross each other before the clock shows 9:30 A.M.?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
Math Expert
Joined: 02 Aug 2009
Posts: 8198
Re: Two people are walking around a circular track. They start at 8 A.M.  [#permalink]

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17 Sep 2019, 19:21
Hovkial wrote:
Two people are walking around a circular track. They start at 8 A.M. from the same point but travel in opposite directions. The first person walks at a speed of two rounds per hour and the second person walks at a speed of three rounds per hour. How many times will they cross each other before the clock shows 9:30 A.M.?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

Combined, they complete 2+3 or 5 rounds in one hour..
Whenever they meet each other, they would have completed one round within themselves, so 5 rounds in 1 hr means they meet 5 times in 1 hr..

If in 1 hr they complete 5 rounds, then in 8:00 - 9:30 am, that is 1.5 hr, they will complete 5*1.5 = 7.5 rounds..

So, they would have met 7 times and on the way to meet 8th time

C
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Re: Two people are walking around a circular track. They start at 8 A.M.   [#permalink] 17 Sep 2019, 19:21
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