Solving 2 Watches with 12 Hour Cycle Problem

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  • Thread starter Thread starter Marcelo Arevalo
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Discussion Overview

The discussion revolves around a problem involving two watches with different rates of time gain and loss, specifically how long it will take for both watches to show the correct time again after being set correctly. The scope includes mathematical reasoning and problem-solving techniques.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks assistance in solving the problem, suggesting the use of the least common multiple (LCM) as a potential approach.
  • Another participant proposes calculating how many days each watch would take to be correct on its own, indicating this might lead to a solution.
  • One participant claims that Watch 1 takes about 360 days to show the correct time again, while Watch 2 takes about 240 days.
  • Based on these calculations, the same participant concludes that the LCM of both watches indicates they will both show the correct time together after 720 days.
  • A later reply confirms this conclusion as correct.

Areas of Agreement / Disagreement

Participants generally agree on the calculations leading to the conclusion that both watches will show the correct time together after 720 days, though the initial problem-solving approach and reasoning are discussed without explicit consensus on the methodology.

Contextual Notes

There may be limitations in the assumptions regarding the rates of gain and loss for the watches, as well as the dependence on the definitions of "correct time" and the implications of the 12-hour cycle.

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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