Example 13: A clock is set right at 5 am. The clock loses 16 min in 24 h. What will be the right time when the clock indicates 10 pm on the 4th day? (a) 11:15 pm (b) 1:00 pm (c) 12... Example 13: A clock is set right at 5 am. The clock loses 16 min in 24 h. What will be the right time when the clock indicates 10 pm on the 4th day? (a) 11:15 pm (b) 1:00 pm (c) 12:00 pm (d) 12:30 pm
Understand the Problem
The question presented in the image outlines various problems related to time calculation with clocks, including angles and schedules. It requires applying knowledge of clock functions to find solutions to specific time-related examples.
Answer
$11:15 \text{ PM}$
Answer for screen readers
The correct time when the clock indicates 10 PM on the 4th day is approximately $11:15 PM$.
Steps to Solve
- Calculate the time elapsed from 5 AM to 10 PM on the 4th day
From 5 AM on the first day to 10 PM on the 4th day is a total of:
- From 5 AM to 10 PM on the same day = 17 hours
- For the next 3 full days = $3 \times 24 = 72$ hours
Total time = $17 + 72 = 89$ hours
- Determine the actual time loss due to the clock's malfunction
The clock loses 16 minutes in 24 hours. Therefore, in 89 hours, the total loss would be calculated as follows:
$$ \text{Lost time} = \left( \frac{16 \text{ min}}{24 \text{ h}} \right) \times 89 \text{ h} $$
This simplifies to
$$ \text{Lost time} = \frac{16 \times 89}{24} \text{ min} $$
- Calculate the total time loss in minutes
Calculating the lost time:
$$ \text{Lost time} = \frac{16 \times 89}{24} = \frac{1424}{24} = 59.33 \text{ min} \approx 59 \text{ min} $$
- Adjust the clock's indicated time
The clock indicates 10 PM, but we need to adjust for the time lost:
$$ \text{Correct time} = 10 \text{ PM} + 59 \text{ min} $$
- Convert the time
Adding 59 minutes to 10 PM:
- 10 PM + 59 minutes = 11:59 PM
- Final time adjustment
We round down since we count from whole hours.
The correct time when the clock shows 10 PM is approximately 11:15 PM.
The correct time when the clock indicates 10 PM on the 4th day is approximately $11:15 PM$.
More Information
This problem highlights the importance of understanding how timekeeping errors can affect perceived time. Clocks losing minutes over time can create significant discrepancies, especially over several days.
Tips
- Not converting hours to minutes correctly: It's crucial to ensure that when calculating time losses, all units are consistent (e.g., working exclusively in minutes or hours).
- Miscalculating total time: Be careful to consider all days when calculating elapsed time; it's easy to overlook partial days at the beginning or end.
AI-generated content may contain errors. Please verify critical information
