If a clock is set correctly at 5 am but loses 16 minutes in 24 hours, what time will it show if it indicates 10 pm on the 4th day?
Understand the Problem
The question is asking us to calculate the time shown by a malfunctioning clock that loses time over a specific period. To solve this, we need to determine how many minutes the clock has lost by the indicated time and adjust the original time accordingly.
Answer
$$ \text{Clock time} = T - 5t $$
Answer for screen readers
The time shown by the clock will be:
$$ \text{Clock time} = T - 5t $$
Steps to Solve
- Identify the time lost per hour
The clock loses 5 minutes every hour. We need to calculate how much time it loses over a specific period.
- Determine the total period in hours
If the question specifies a certain timeframe (e.g., several hours), we can denote this as $t$ hours.
- Calculate the total time lost
To find out how much time the clock has lost, we multiply the time lost per hour by the total number of hours:
$$ \text{Total time lost} = 5 \text{ minutes/hour} \times t \text{ hours} $$
- Adjust the original time
Assuming the original correct time is $T$, the time shown on the clock after $t$ hours will be:
$$ \text{Clock time} = T - \text{Total time lost} $$
This equation gives us the actual time displayed by the malfunctioning clock.
The time shown by the clock will be:
$$ \text{Clock time} = T - 5t $$
More Information
This problem illustrates the concept of time management and tracking discrepancies in devices that are supposed to keep accurate time. It's interesting to note how small errors can accumulate over time leading to significant differences.
Tips
- Confusing the total time lost with the total time elapsed. Always remember to differentiate between the two.
- Forgetting to convert the units if the time period is given in hours and you need to calculate minutes lost.
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