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Pat's watch and Kim's watch

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by Needgmat » Wed Aug 31, 2016 10:05 am
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 the correct time at 8 o'clock in the morning and run without interruption, after 72 hours, what will be the difference in the 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

OAE

Please explain
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by GMATGuruNY » Wed Aug 31, 2016 10:16 am
Needgmat wrote: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 the correct time at 8 o'clock in the morning and run without interruption, after 72 hours, what will be the difference in the 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 6 hours:
Since Pat's watch gains 10 seconds every 2 hours, Pat's watch will gain a total of 30 seconds.
Since Kim's watch loses 5 seconds every 3 hours, Kim's watch will lose a total of 10 seconds.
Thus, the time difference between the two watches = 30+10 = 40 seconds.

Over 72 hours, there will be 12 6-hour intervals.
Since each of the 12 6-hour intervals will yield a time difference of 40 seconds, the total time difference after 72 hours = 12*40 = 480 seconds = 8 minutes.

The correct answer is E.
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by Needgmat » Thu Sep 01, 2016 8:48 am
In 6 hours:
Since Pat's watch gains 10 seconds every 2 hours, Pat's watch will gain a total of 30 seconds.
Since Kim's watch loses 5 seconds every 3 hours, Kim's watch will lose a total of 10 seconds.
Thus, the time difference between the two watches = 30+10 = 40 seconds.

Hi GMATGuruNY ,

Thank you so much for your explanation.

Just a quick question. Can you please explain why 30+10, as we have to find the difference between so why not 30-10?

Please explain.

Many thanks in advance.

Kavin
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by [email protected] » Thu Sep 01, 2016 10:03 am
Hi Needgmat,

Since Pat's watch is 30 seconds AHEAD and Kim's watch is 10 seconds BEHIND, the difference is 30 - (-10) = 40 seconds.

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by GMATGuruNY » Thu Sep 01, 2016 10:10 am
Needgmat wrote:
In 6 hours:
Since Pat's watch gains 10 seconds every 2 hours, Pat's watch will gain a total of 30 seconds.
Since Kim's watch loses 5 seconds every 3 hours, Kim's watch will lose a total of 10 seconds.
Thus, the time difference between the two watches = 30+10 = 40 seconds.

Hi GMATGuruNY ,

Thank you so much for your explanation.

Just a quick question. Can you please explain why 30+10, as we have to find the difference between so why not 30-10?

Please explain.

Many thanks in advance.

Kavin
Let's say the start time is 12am.
Pat's watch GAINS 30 seconds every 6 hours, so at 6am Pat's watch shows the following time:
6am + 30 seconds = 6:00:30.
Kim's watch LOSES 10 seconds every 6 hours, so at 6am Kim's watch shows the following time:
6am - 10 seconds = 5:59:50.
Thus, the time difference every 6 hours = (6:00:30) - (5:59:50) = 40 seconds.
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by Matt@VeritasPrep » Thu Sep 01, 2016 4:37 pm
Needgmat wrote: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 the correct time at 8 o'clock in the morning and run without interruption, after 72 hours, what will be the difference in the 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

OAE

Please explain
You could also use the plain old Distance = Rate * Time equation. Here, we'll say that

D = How far ahead Pat's watch is
R = How much faster Pat's watch runs per hour = Pat's watch - Kim's watch
T = 72 hours

We know that Pat gains 5 seconds per hour and Kim loses (5/3) seconds per hour, so R = 5 - (5/3), or 20/3.

Then, we just use our equation

D = R * T

D = (20/3) * 72

D = 20 * 24 => 480

480 seconds is the same as 8 minutes, so Pat is 8 minutes ahead.
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