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Sarah and James are running around a circular track. Sa

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Sarah and James are running around a circular track. Sa  [#permalink]

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New post 22 Nov 2018, 10:57
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Sarah and James are running around a circular track. Sarah runs at a constant speed of 800 feet/minute and James runs at a constant speed of 1200 feet/minute. James is currently 80 feet behind Sarah, how many seconds will it take James to catch up to Sarah and run 40 feet ahead of her?

A. 5 Seconds

B. 10 Seconds

C. 18 Seconds

D. 40 Seconds

E. 50 Seconds
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Sarah and James are running around a circular track. Sa  [#permalink]

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New post 22 Nov 2018, 20:18
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What is the source of this question?

Have to be careful with the information. Not only does he start 80ft behind, he also needs to get 40ft in front.
80+40=120. Rewriting the question: How many seconds does it take for James to gain 120ft on Sarah?

Speed·time=distance
Since there are two speeds and we are trying to find the difference between the speeds

(\(Speed_J\) - \(Speed_S\))·time=distance

\(\frac{1200ft}{min}- \frac{800ft}{min}·x = 120ft\)

\(x(\frac{400ft}{min}) = 120ft\)

\(\frac{x400ft}{min} = 120ft\)

We want to eliminate the feet units, so swap the denominator and the distance

\(\frac{x400ft}{120ft} = 1 min\)

Can now cancel units

\(\frac{x400}{120}=60 seconds\)

\(\frac{10x}{3}=60 seconds\)

10x=180 seconds

x=18 seconds

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Re: Sarah and James are running around a circular track. Sa  [#permalink]

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New post 22 Nov 2018, 21:00
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Jazzmin wrote:
Sarah and James are running around a circular track. Sarah runs at a constant speed of 800 feet/minute and James runs at a constant speed of 1200 feet/minute. James is currently 80 feet behind Sarah, how many seconds will it take James to catch up to Sarah and run 40 feet ahead of her?

A. 5 Seconds

B. 10 Seconds

C. 18 Seconds

D. 40 Seconds

E. 50 Seconds


Right now, James is 80 feet behind. He needs to be 40 feet ahead. So he needs to cover a relative distance of 80 + 40 = 120 feet.

Time taken = Relative distance/Relative Speed = 120/(1200 - 800) = 120/400 mins = 120/400 * 60 sec = 18 sec

Answer (C)

Note that the fact that they are running in a circle doesn't have much to do here.

Check this post on relative speed: https://www.veritasprep.com/blog/2012/0 ... elatively/
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Re: Sarah and James are running around a circular track. Sa  [#permalink]

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New post 02 Oct 2019, 19:38
relative distance ; 80+40 ; 120 feet
relative speed ; 1200-800 ; 400 ft/min
time 120/400 ; .3*60 ; 18 sec
IMO C

Jazzmin wrote:
Sarah and James are running around a circular track. Sarah runs at a constant speed of 800 feet/minute and James runs at a constant speed of 1200 feet/minute. James is currently 80 feet behind Sarah, how many seconds will it take James to catch up to Sarah and run 40 feet ahead of her?

A. 5 Seconds

B. 10 Seconds

C. 18 Seconds

D. 40 Seconds

E. 50 Seconds
GMAT Club Bot
Re: Sarah and James are running around a circular track. Sa   [#permalink] 02 Oct 2019, 19:38
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Sarah and James are running around a circular track. Sa

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