Understanding Clock Gain and True Time Calculation

In the world of timekeeping, understanding how clocks gain time and the true time calculation can be quite intriguing. Letrsquo;s explore a few scenarios to clarify the concept with practical examples.

Scenario 1: Clock Gains 5 Minutes Every Hour

Letrsquo;s consider a clock that gains 5 minutes every hour. If we set this clock correctly at 5 AM, and it shows 10 AM, what is the actual time?

To solve this, we need to follow these steps:

Calculate the total time the clock shows from 5 AM to 10 AM:

The clock shows a total of 5 hours from 5 AM to 10 AM.

Calculate how many minutes the clock gains in that time:

The clock gains 5 minutes for every hour. Over 5 hours, it will gain: 5 minutes/hour x 5 hours 25 minutes.

Calculate the total time that has actually passed:

When the clock shows 10 AM, it has actually gained 25 minutes. The actual time elapsed is: 5 hours - 25 minutes 4 hours and 35 minutes. From 5 AM, 4 hours and 35 minutes later is 9:35 AM.

Thus, when the clock shows 10 AM, the actual time is 9:35 AM.

Scenario 2: Clock Gains 4 Minutes Every Hour

Now, letrsquo;s explore another scenario where a clock gains 4 minutes every hour. If the clock indicates 10 AM, what is the true time?

Calculate how often the clock gains minutes:

For every hour, the clock gains 4 minutes. 1 minute per 15 minutes means: 60/4 15 minutes per minute gain.

Calculate how much the clock will have gained by 10 AM:

By 10 AM, the clock would have gained 16 minutes. This means the clock is 16 minutes ahead of the true time.

Determine the correct time:

Since the clock is 16 minutes ahead, the true time is 16 minutes before 10 AM. The true time would be 10:16 AM - 16 minutes 9:45 AM.

Thus, when the clock shows 10 AM, the actual time is 9:45 AM.

Note: This scenario and the previous one necessitate the understanding of how clock gains are cumulative over time.

Additional Scenario: Clock Gaining 4 Minutes Every Hour on a Wednesday

Letrsquo;s extend our scenario to a hypothetical Wednesday:

Scenario: A clock is set right at 6 AM on Wednesday. The clock gains 4 minutes in 1 hour. What will be the true time when the clock indicates 10 AM on the following day?

Presuming you mean the following day and not the following Wednesday, we can calculate the true time as follows:

Calculate the cumulative gain by 10 AM on the next day:

From 6 AM to 10 AM, the clock will gain 4 minutes every hour for 4 hours. The total gain by 10 AM is: 4 minutes/hour x 4 hours 16 minutes.

Determine the true time:

The clock is 16 minutes ahead, so the true time is 16 minutes before 10 AM. The true time is 10:16 AM - 16 minutes 9:45 AM.

Thus, when the clock shows 10 AM on the following day, the actual time is 9:45 AM.

Conclusion: Understanding clock gains and true time calculation involves accurate steps and can help in resolving time discrepancies. The scenarios provided offer a practical insight into how to approach such problems.