Calculating the Time on a Watch that Loses 2 Minutes Every Hour: A Comprehensive Guide

Often, the accuracy of a watch can be an important consideration, especially when the time discrepancy is significant. Let's explore a scenario involving a watch that loses 2 minutes every hour. We will derive a formula to calculate the time on this watch, given that its initial setting is 9 AM and the correct time is 4 PM the next day.

Understanding the Scenario

Suppose you have a watch correctly set at 9 AM. If this watch loses 2 minutes every hour, how will the time be displayed on this watch when the correct time is 4 PM the next day? We break down the calculation step by step to understand the time discrepancy.

Step-by-Step Calculation

1. Determine the Total Time Elapsed

To find the total time elapsed, we calculate:

From 9 AM today to 9 AM the next day is 24 hours. From 9 AM to 4 PM on the next day is an additional 7 hours.

Therefore, the total time elapsed is 24 7 31 hours.

2. Calculate the Total Time Lost by the Watch

The watch loses 2 minutes every hour. Over 31 hours, the total time lost is:

31 hours × 2 minutes/hour 62 minutes

3. Convert the Lost Time into Hours and Minutes

62 minutes equates to 1 hour and 2 minutes.

4. Determine the Final Time on the Watch

The correct time after 31 hours is 4 PM the next day. To find out what time the faulty watch will show, we subtract the lost time from the correct time:

4 PM - 1 hour 3 PM. 3 PM - 2 minutes 2:58 PM.

Therefore, when the correct time is 4 PM the next day, the faulty watch will show 2:58 PM.

Additional Scenarios

Calculation for a Shorter Period

For a shorter period, consider the time from 9 AM today to 10 PM on the same day. The calculation is:

From 9 AM to 10 PM is 13 hours. The watch loses 2 minutes every hour, so over 13 hours, it will lose:

13 hours × 2 minutes/hour 26 minutes.

Therefore, the time showing on the faulty watch at 10 PM would be:

10 PM - 26 minutes 9:34 PM.

Comprehensive Table of Time Loss

Here is a table showing the time loss for each hour from 10 AM to 4 PM the next day:

Correct Time Time on Faulty Watch 10 AM 9:58 AM 11 AM 10:56 AM 12 PM 11:54 AM 1 PM 12:52 PM 2 PM 1:50 PM 3 PM 2:48 PM 4 PM 3:46 PM 5 PM 4:44 PM 6 PM 5:42 PM 7 PM 6:40 PM 8 PM 7:38 PM 9 PM 8:36 PM 10 PM 9:34 PM 11 PM 10:32 PM 12 AM 11:30 PM 1 AM 12:28 AM 2 AM 1:26 AM 3 AM 2:24 AM 4 AM 3:22 AM 5 AM 4:20 AM 6 AM 5:18 AM 7 AM 6:16 AM 8 AM 7:14 AM 9 AM 8:12 AM 10 AM 9:10 AM 11 AM 10:08 AM 12 PM 11:06 AM 1 PM 12:04 PM 2 PM 1:02 PM 3 PM 2:00 PM 4 PM 2:58 PM

Conclusion

User experience in timekeeping can be significantly affected by inaccuracy. Understanding the mechanics behind a watch that loses time is valuable for various applications, such as time management and reliability assurance. The calculation method provided here can be applied to different scenarios, allowing for precise time management in situations where accuracy is crucial.