Understanding the Time Display of a Clock Gradually Gaining Time per Hour

In many real-world scenarios, clocks can gain or lose time over a period. This problem explores the phenomenon of a clock gaining time gradually. We need to determine the time shown on a clock that gains 3.5 minutes per hour from 6:00 AM to 6:00 PM on the same day.

Initial Conditions

The clock is set correctly at 6:00 AM.

Time Calculation

From 6:00 AM to 6:00 PM, the span of time is 12 hours. We are informed that the clock gains 3.5 minutes every hour. To understand the total gain, we calculate the total minutes gained over the 12-hour period:

Calculation Steps

Determine the number of hours: 12 hours. Calculate the gain per hour: 3.5 minutes. Multiply the number of hours by the gain per hour: 12 hours * 3.5 minutes/hour 42 minutes. Add the gained minutes to the initial time: 6:00 PM 42 minutes 6:42 PM.

Thus, the clock will display 6:42 PM on the same day when it was set correctly at 6:00 AM and gains 3.5 minutes per hour.

Conclusion

The clock initially set at 6:00 AM will show a time of 6:42 PM on the same day if it gains 3.5 minutes per hour. This calculation can be applied to similar scenarios where a clock's time gain is consistent over a specific period.