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### Watch Gaining Time

```Date: 11/10/2002 at 00:18:24
From: Ann
Subject: Watch gaining time

A watch gains six minutes every hour. If the time of this watch is
set accurately at midnight, and the watch now shows 8:26 a.m., if the
watch stopped 30 minutes ago, what's the correct time now?
```

```
Date: 11/10/2002 at 18:03:04
From: Doctor Ian
Subject: Re: Watch gaining time

Hi Ann,

If the watch gains 6 minutes per hour, that's 360 seconds every 3600
seconds, or 1 second every 10 seconds.

In other words, the clock is running 10% fast. We can use this to
figure out what the actual time is from the displayed time. For
example, suppose the watch reads 3:18. What's the actual time?

Well, 3:18 is 3 hours + 18 minutes, which is 180 + 18 minutes, or 198
minutes. This must be the actual time, T, plus 10 percent, so

T + T/10 = 198

(11/10)T = 198

T = 198 * (10/11)

= 180 minutes

or exactly 3:00.

Can you take it from here? Try doing the same thing that I did, but
instead of using 198 minutes, use the number of minutes from midnight
to 8:26, instead of to 3:18.

(You'll have to convert 8 hours and 26 minutes minutes to some total
number of minutes.)

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Calendars/Dates/Time
Middle School Word Problems

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