Solving 2 Watches with 12 Hour Cycle Problem

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  • Thread starter Marcelo Arevalo
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In summary, it would take 720 days for both watches to next together tell the correct time if one gains 2 minutes and the other loses 3 minutes each day in a 12 hour cycle. This can be calculated by finding the least common multiple (LCM) of the days it takes for each watch to be correct on its own.
  • #1
Marcelo Arevalo
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Can you help me please on these problem.

"I have 2 watches with a 12 hour cycle. One gains 2 minutes a day and the other loses 3 minutes a day. If I set them at the correct time, how many days will it be before they next together tell the correct time? "my idea of solving it is using LCM, bu t I can't get my thoughts to come together. please, kindly help.
thank you.
 
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  • #2
Marcelo Arevalo said:
Can you help me please on these problem.

"I have 2 watches with a 12 hour cycle. One gains 2 minutes a day and the other loses 3 minutes a day. If I set them at the correct time, how many days will it be before they next together tell the correct time? "my idea of solving it is using LCM, bu t I can't get my thoughts to come together. please, kindly help.
thank you.

I think you're on the right track here. Why don't you calculate how many days each watch would take to be correct again on their own? So, Watch 1 on its own takes how many days to be correct again? Watch 2 on its own takes how many days to be correct again? That might suggest something to you.
 
  • #3
Watch 1 takes about 360 days to tell correct time again
Watch 2 takes about 240 days to tell correct time again

getting the LCM of both watches ; together they need 720 days for both to tell correct time.

Is it correct??
answer is 720 days.
 
  • #4
Yes, it is correct.
 

Related to Solving 2 Watches with 12 Hour Cycle Problem

1. How do you solve the 2 watches with 12 hour cycle problem?

The solution to this problem involves setting one watch to the correct time and then using the other watch to track the passing hours. For example, if one watch is set to 12:00 PM, the second watch can be set to 12:00 AM. As the first watch moves through the hours, the second watch can be used to track the passing hours by setting it forward or backward by one hour for each hour that passes on the first watch.

2. What is the purpose of solving the 2 watches with 12 hour cycle problem?

The purpose of this problem is to demonstrate the concept of time synchronization and how two objects with different cycles or speeds can be used to accurately track time.

3. Can this problem be applied to real-life scenarios?

Yes, this problem can be applied to real-life scenarios, such as using two clocks in different time zones to accurately track time in both locations.

4. Are there any variations of this problem?

Yes, there are variations of this problem, such as using two watches with different cycle lengths (e.g. one watch with a 24 hour cycle and one watch with a 12 hour cycle) or using more than two watches to track time.

5. What other concepts can be learned from solving the 2 watches with 12 hour cycle problem?

Solving this problem can also help to improve logical thinking and problem-solving skills, as well as understanding the concept of cycles and how they can be used to measure time.

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