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# Pat's watch gains an extra 10 seconds every 2 hours. Kim's

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Pat's watch gains an extra 10 seconds every 2 hours. Kim's [#permalink]  24 Mar 2013, 09:47
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Pat's watch gains an extra 10 seconds every 2 hours. Kim's watch loses 5 seconds every 3 hours. If both watches are set to correct time at 8 o'clock in the morning and run without interruption, after 72 hours, what will be the difference in time between Pat's watch and Kim's watch?

(A) 4 min

(B) 6 min

(C) 6 min 40 sec

(D) 7 min 30 sec

(E) 8 min
[Reveal] Spoiler: OA

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Re: Pat's watch gains an extra 10 seconds every 2 hours. Kim's [#permalink]  24 Mar 2013, 09:53
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In 72 hours Pat's watch will gain 360 seconds, since in 2 hours it gains 10 seconds, that means in 1 hour 5 seconds and in 72 hours 72*5 seconds, i.e. 360 seconds or 6 mins.
Kim's watch loses 5 seconds in 3 hours, in 72 hours it will loose 72/3 * 5 = 24*5 = 120 seconds = 2 mins.
Total difference 6 - (-2, it lost 2 mins ) = 6 + 2 = 8 mins.

Please give a kudo if you like my explanation.
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Re: Pat's watch gains an extra 10 seconds every 2 hours. Kim's [#permalink]  24 Mar 2013, 10:11
First we have to bring everything to the same scale, to make life easier:

$$10 sec ->2h = 5 sec -> 1h$$
$$5 sec->3h = \frac{5}{3}sec->1h$$

Pat's watch will gain a total of $$5 sec * 72 h = 360 sec$$
Kim's watch will lose a total of$$5/3 sec * 72 h = 120 sec$$

<----------------|-------------------->
(-120sec)----- 0------------( +360 sec)

tot distance = $$120+360=480 sec = 8 min$$

E
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Re: Pat's watch gains an extra 10 seconds every 2 hours. Kim's [#permalink]  24 Mar 2013, 13:39
This is how I solved this..

10s/2h, 72/2 -> 36 (and then the /h value x10) -> 36x10 = 360. Go on with /6 -> 6min
5s/3h, 72/3 -> 24 (and then the /h value x5) -> 36x5 = 120. Go on with /6 -> 2 (sine it's a loss it's -2)

-2 to 6 = 8, hence E (I did not get it right first since I personally missed the "loss")
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Pat's watch gains an extra 10 seconds every 2 hours. Kim's [#permalink]  14 Jul 2014, 22:17
Bunuel,

This question is using a kind of Relative velocity fundamental, but is put forward in a different manner. Opposite speeds do add up in relative calculations.
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Last edited by honchos on 12 Nov 2014, 10:57, edited 4 times in total.
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Re: Pat's watch gains an extra 10 seconds every 2 hours. Kim's [#permalink]  15 Jul 2014, 01:46
Expert's post
honchos wrote:
Bunuel,

Can you Please solve this question.

Pat's watch gains an extra 10 seconds every 2 hours. Kim's watch loses 5 seconds every 3 hours. If both watches are set to correct time at 8 o'clock in the morning and run without interruption, after 72 hours, what will be the difference in time between Pat's watch and Kim's watch?

(A) 4 min

(B) 6 min

(C) 6 min 40 sec

(D) 7 min 30 sec

(E) 8 min

In 72 hours Pat's watch will gain an extra 72/2*10 = 360 seconds.

In 72 hours Kim's watch will lose 72/3*5 = 120 seconds.

Hence the difference will be 360 + 120 = 480 seconds or 8 minutes.

Hope it helps.
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Re: Pat's watch gains an extra 10 seconds every 2 hours. Kim's   [#permalink] 15 Jul 2014, 01:46
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