Solving 2 Watches with 12 Hour Cycle Problem

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SUMMARY

The problem involves two watches with a 12-hour cycle, where one watch gains 2 minutes per day and the other loses 3 minutes per day. After calculating the time it takes for each watch to show the correct time again, it is determined that Watch 1 takes 360 days and Watch 2 takes 240 days. The least common multiple (LCM) of these two periods is 720 days, which is the time required for both watches to display the correct time simultaneously again.

PREREQUISITES
  • Understanding of time cycles and how they affect clock accuracy
  • Knowledge of calculating least common multiples (LCM)
  • Basic arithmetic operations involving addition and subtraction of time
  • Familiarity with the concept of time gain and loss in clocks
NEXT STEPS
  • Study the mathematical principles behind least common multiples (LCM)
  • Explore timekeeping mechanisms and how they can gain or lose time
  • Investigate real-world implications of clock inaccuracies in various fields
  • Learn about other time-related problems and their solutions in mathematics
USEFUL FOR

Mathematicians, educators, students studying time-related problems, and anyone interested in clock mechanics and accuracy issues.

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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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.
 
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.
 
Yes, it is correct.
 

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