The first clock is slow and loses 1 minute every hour.
The second clock is fast and gains 1 minute every hour.
At 12:00 noon, both clocks show the same time. What time will it be when the two clocks show the same time again?
The Two Clocks Riddle
Hint:
The key to solving this is realizing that the time difference between the two clocks will increase by 2 minutes every hour. Since one clock gains 1 minute per hour and the other loses 1 minute per hour, the two clocks are getting 2 minutes further apart each hour.
Start by thinking about how long it will take for the difference between the two clocks to reach an exact multiple of 12 hours (since the clocks show the same time at 12:00 noon). Once you determine how long it takes for the clocks to match again, you’ll know the exact time.
The first clock is slow and loses 1 minute every hour.
The second clock is fast and gains 1 minute every hour.
At 12:00 noon, both clocks show the same time.
Since the two clocks are 1 minute apart every hour (because one is gaining 1 minute and the other is losing 1 minute), the difference between them increases by 2 minutes per hour.
How to Find the Time When They Match Again:
Let’s find when the clocks will show the same time again. Since the clocks are 2 minutes apart every hour, we need to find when that difference will be a multiple of 12 hours.
In 12 hours, the difference between the two clocks will be 24 minutes (2 minutes per hour × 12 hours).
After 24 hours, the difference will be 48 minutes, and so on.
Now, we know the clocks will show the same time again after 12 hours because the relative difference between them is 24 minutes (which is a multiple of 12 hours). So, the time when the clocks will show the same time again is 12 hours later:
Answer:
The two clocks will show the same time again at 12:00 midnight
