Question

If a clock gets slow by 5 minutes every hour, and it was correct at 6 AM on Monday, what will be the time at 6 PM on Tuesday?

Hint:

First count the real hours from Monday morning to Tuesday evening. Either calculate the total minutes lost or multiply the real interval by the clock rate $55/60$.

Answer 1

Step 1: Calculate the total actual time passed.
From Monday 6 AM to Tuesday 6 PM, the total time elapsed is:
\[ 24 + 12 = 36 \text{ hours} \]
Step 2: Determine the speed of the clock.
The clock loses 5 minutes every hour, so in 60 minutes it shows only 55 minutes.
Thus, the clock runs at \( \frac{55}{60} \) of real time.
Step 3: Find the time shown by the clock.
Time shown by the clock in 36 hours:
\[ 36 \times \frac{55}{60} = 33 \text{ hours} \]
Step 4: Calculate the final time.
Starting from 6 AM Monday, adding 33 hours gives:
\[ 6 \text{ AM} + 33 \text{ hours} = 3 \text{ PM (Tuesday)} \]
Step 5: Conclusion.
The clock will show 3 PM.

Answer 2

Concept:

• A slow clock loses a fixed number of minutes during every real hour.
• Total loss can be subtracted from the correct finishing time.

Step 1: Find the real elapsed time.
From Monday $6$ AM to Tuesday $6$ PM, $24+12=36$ hours pass.

Step 2: Calculate the accumulated loss.
The clock loses $5$ minutes per hour, so it loses $36\times5=180$ minutes, which is $3$ hours.

Step 3: Adjust the correct time.
At actual Tuesday $6$ PM, the slow clock is $3$ hours behind. It therefore shows Tuesday $3$ PM.

Final Answer: Tuesday, $3$ PM