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# Marla starts running around a circular track at the same

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Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
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Marla starts running around a circular track at the same [#permalink]

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16 Mar 2012, 07:55
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Difficulty:

35% (medium)

Question Stats:

74% (01:53) correct 26% (02:04) wrong based on 550 sessions

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Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 32 laps around the track per hour and Nick completes 12 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?

(A) 5
(B) 8
(C) 12
(D) 15
(E) 20

How to do this guys?
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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Re: Marla starts running around a circular track at the same [#permalink]

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16 Mar 2012, 09:26
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enigma123 wrote:
Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 32 laps around the track per hour and Nick completes 12 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?

(A) 5
(B) 8
(C) 12
(D) 15
(E) 20

How to do this guys?

Marla completes 32-20=20 more laps in 1 hour. Marla to complete 4 (20/5=4) more laps will need 1/5 hours, which is 12 minutes.

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Manager
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Re: Marla starts running around a circular track at the same [#permalink]

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16 Mar 2012, 11:00
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Marla completes 32laps/60min, Nick completes 12laps/60mins.
After x mins Marla would have completed 4 laps more than Nick had completed.
x((32-12)/60) = 4,
x*20/60 = 4,
x = 12 mins.
Director
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Re: Marla starts running around a circular track at the same [#permalink]

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16 Mar 2012, 16:46
Bunuel - how did you get this?

Marla to complete 4 (20/5=4) more laps will need 1/5 hours, which is 12 minutes.
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Posts: 44319
Re: Marla starts running around a circular track at the same [#permalink]

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16 Mar 2012, 16:53
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Expert's post
enigma123 wrote:
Bunuel - how did you get this?

Marla to complete 4 (20/5=4) more laps will need 1/5 hours, which is 12 minutes.

Since Marla completes 20 more laps in 1 hour, then to complete 1/5 th of 20 laps (4 laps) she will need 1/5 th of an hour, which is 12 minutes.
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Re: Marla starts running around a circular track at the same [#permalink]

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17 Mar 2012, 07:06
Best way is to use plug in!

Always plug in C first, since this is the median value!

In 12 minutes she will have completed 32/5 rounds ( /5 because 12min is 1/5 hours) and he will have completed 12/5 rounds.

32/5 = 6 2/5
12/5 = 2 2/5

4 is the difference and hence C is th answer.

Sometimes you get lucky and plug in the right answer first! Will help you save heaps of time!
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Re: Marla starts running around a circular track at the same [#permalink]

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12 Apr 2012, 04:35
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Maria's rate - 32 laps per hour --> 32/60 laps/min
Nick's rate - 12 laps per hour --> 12/60 laps/min

lets set equations:

32/60*t=4 (since Maria had to run 4 laps before Nick would start)
12/60*t=0 (Hick has just started and hasn't run any lap yet)
-----------------------------------
(32/60-12/60)*t=4-0 (since Nick was chasing Maria)
t=12 min needed Maria to run 4 laps
Senior Manager
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Re: Marla starts running around a circular track at the same [#permalink]

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23 Apr 2012, 15:27
I say C. 12 mins.

Marla's speed : 32/60 laps per min
Nick's speed : 12/60 laps per min

So by plugging in ans choices,

at 12 mins, Marla : 6.4 laps, Nick 2.4 laps.
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Joined: 06 Mar 2012
Posts: 33
Re: Marla starts running around a circular track at the same [#permalink]

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23 Apr 2012, 21:50
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I also got C (12).

t= time
32 laps per hour * t = 12 laps per hour * t + 4 laps

32t = 12t + 4
20t = 4
t= 1/5 hr

1/5(60min)= 12 mins

I believe the recommended strategy is to change to minutes right away but in this situation I found it easier to do it at the end because of how the rates simplified per minute.
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Re: Marla starts running around a circular track at the same [#permalink]

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23 Apr 2012, 22:28
In 15 min - Marla has completed 32/4 = 8 laps and Nick -> 12/4 = 3
the difference at 15 mins is 5 laps. So plugging in C.

In 12 mins - Marla has completed 32/5 = 6.4laps while Nick has completed 12/5 = 2.4 laps , a difference of 4 laps.

So ans - C
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Re: Marla starts running around a circular track at the same [#permalink]

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23 Apr 2012, 23:32
In 1 min:
Marla runs: 32/60 = 8/15 laps
Nick walks: 12/60 = 1/5 laps

Let x be the number of minutes required for Marla to be 4 laps ahead of Nick.
x * 1/5 + 4 = x * 8/15
x =12 mins
Intern
Joined: 29 Feb 2012
Posts: 10
Re: Marla starts running around a circular track at the same [#permalink]

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25 Apr 2012, 02:21
use relative velocity to solve it

the relative velocity would be (32-12) in 1 hour.
hence, 20 laps in 1 hour
therefore time to complete four laps is 1/5hr
12 mins
Manager
Joined: 11 Sep 2013
Posts: 158
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Re: Marla starts running around a circular track at the same [#permalink]

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21 Apr 2014, 02:10
Let time be t
32/60t-12/60t=4 so t=12
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Re: Marla starts running around a circular track at the same [#permalink]

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21 Apr 2014, 23:01
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Let the one lap distance = d
Speed of Marla $$= \frac{32}{60}$$
Speed of Nick $$= \frac{12}{60}$$
Time t would be same in both the cases

Setting up the equation

$$d = \frac{32}{60}* t$$ ............ (1)

$$d-4 = \frac{12}{60} * t$$........(2)

Equating (1) & (2)

$$\frac{12}{60} * t + 4 = \frac{32}{60} * t$$

$$\frac{1}{3} * t = 4$$

t = 12

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Re: Marla starts running around a circular track at the same [#permalink]

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02 May 2014, 03:43
Bunuel wrote:
enigma123 wrote:
Bunuel - how did you get this?

Marla to complete 4 (20/5=4) more laps will need 1/5 hours, which is 12 minutes.

Since Marla completes 20 more laps in 1 hour, then to complete 1/5 th of 20 laps (4 laps) she will need 1/5 th of an hour, which is 12 minutes.

I believe you used the concept of relative speed over here as well Bunuel . Isn't it so ? Relative speed of Bunue is 20 laps/hr so 4 laps in 1/5 of an hr = 12 minutes
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Re: Marla starts running around a circular track at the same [#permalink]

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27 Dec 2015, 12:57
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marla runs 32/60=8/15 laps per minute
nick walks 12/60=3/15 laps per minute
marla gains 8/15-3/15=1/3 laps per minute
4 laps/1/3 lap per minute=12 minutes
Intern
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Marla starts running around a circular track at the same [#permalink]

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23 Mar 2017, 14:39
Why to make it more difficult than it is?

Marla walks 32 laps in 1 hour and spends x hours on the road. Laps covered = 32x
Nick walks 12 laps in 1 hour and spends x hours on the road. Laps covered = 12x (which must be 4 laps fewer than Marla)

32x-12x=4
x=0.2h=12 min (C)
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Marla starts running around a circular track at the same [#permalink]

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26 Sep 2017, 10:43
Given, the distance traveled by Marla in 60 minutes = 32
Distance traveled by Marla in 't' mins = $$\frac{32t}{60}$$

Also given, the distance traveled by Nick in 60 minutes = 12
Distance traveled by Nick in 't' mins = $$\frac{12t}{60}$$

Prompt says there will be a difference of 4 laps at some point in time between the above two distances.

Since Maria travels faster, the distance covered by Maria will be more than the distance covered by Nick. Therefore, subtract the distance traveled by Nick from the distance traveled by Maria in order to avoid a negative resultant.

$$\frac{32t}{60}$$ - $$\frac{12t}{60}$$ = 4

Solving,
$$\frac{20t}{60}$$ = 4
$$\frac{t}{3}$$ = 4

t= 12 mins.
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Re: Marla starts running around a circular track at the same [#permalink]

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29 Sep 2017, 10:33
enigma123 wrote:
Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 32 laps around the track per hour and Nick completes 12 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?

(A) 5
(B) 8
(C) 12
(D) 15
(E) 20

We can use the following formula:

time = change in distance/change in rate

time = 4/20 = 1/5 hour = 12 minutes

Alternate Solution:

Note that Marla’s rate is 32/60 laps per minute and Nick’s rate is 12/60 laps per minute. Let’s say after t minutes, Marla completes 4 more laps than Nick. Then, in t minutes Marla completes 32t/60 laps and Nick completes 12t/60 laps. Since the number of laps completed by Marla is 4 more than the number completed by Nick, we have:

32t/60 = 12t/60 + 4

32t/60 - 12t/60 = 4

20t/60 = 4

t/3 = 4

t = 12

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Re: Marla starts running around a circular track at the same   [#permalink] 29 Sep 2017, 10:33
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