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Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds

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Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds  [#permalink]

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New post 06 Sep 2018, 10:03
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A
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E

Difficulty:

  95% (hard)

Question Stats:

30% (02:50) correct 70% (02:37) wrong based on 86 sessions

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Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds every 30 minutes. If they set their watches correctly at 10:00 am, after how many hours will the two watches show the same time again?

A- 360 hours

B- 720 hours

C- 1080 hours

D- 1440 hours

E- 2160 hours

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Re: Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds  [#permalink]

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New post 06 Sep 2018, 17:56
rohan2345 wrote:
Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds every 30 minutes. If they set their watches correctly at 10:00 am, after how many hours will the two watches show the same time again?

A- 360 hours

B- 720 hours

C- 1080 hours

D- 1440 hours

E- 2160 hours


Jack's way h gains 10 secs and Jose's loses 15 sec in 30 min or 30 secs in 1 HR..
So the difference in 1 HR is 40 secs..

Now since it is given 10:00 am and asks for the same time again, it means a difference of 24 hrs since we are taking AM in consideration otherwise it would have been 12 hrs..

So if 40sec in 1hr, 24 hour in 24*60*60/40=2160 hrs
Had it been 10:00 to 10:00 that is 12 hrs ana will be 2160/2=1080

But as per the wordings of question Ans should be 2160..
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Re: Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds  [#permalink]

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New post 15 Jan 2019, 03:45
What does it really mean when the question uses the terms "gains" and "loses" ?
I figured that it would be a concept of relative speed but could not make out that the speeds will be added even if they move in the same direction.
If one is gaining and the other is loosing and there is only a clockwise rotation possible in case of a watch, would it not be in opposite directions ?
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Re: Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds  [#permalink]

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New post 16 Jan 2019, 13:17
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Top Contributor
rohan2345 wrote:
Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds every 30 minutes. If they set their watches correctly at 10:00 am, after how many hours will the two watches show the same time again?

A- 360 hours
B- 720 hours
C- 1080 hours
D- 1440 hours
E- 2160 hours


Jacks watch GAINS 10 seconds every HOUR.

Jose’s watch loses 15 seconds every 30 minutes
This means Jose’s watch LOSES 30 seconds every HOUR

In 1 HOUR, the time difference between the two watches is 40 seconds
So, in 2 HOURS, the time difference between the two watches is 80 seconds
So, in 3 HOURS, the time difference between the two watches is 120 seconds
Or we can say:, in 3 HOURS, the time difference between the two watches is 2 MINUTES
So, in 90 HOURS, the time difference between the two watches is 60 MINUTES
In other words, in 90 HOURS, the time difference between the two watches is 1 HOUR

KEY CONCEPT: In order for their watches to show the same time, we need a time difference of 24 HOURS
We know that, in 90 HOURS, the time difference between the two watches is 1 HOUR

Multiple both values by 24 to get: in 2160 HOURS, the time difference between the two watches is 24 HOURS

Answer: E

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Brent
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Re: Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds   [#permalink] 16 Jan 2019, 13:17
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Jacks watch gains 10 seconds every hour. Jose’s watch loses 15 seconds

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