MHB Solving 2 Watches with 12 Hour Cycle Problem

  • Thread starter Thread starter Marcelo Arevalo
  • Start date Start date
  • Tags Tags
    Cycle
AI Thread Summary
Two watches with a 12-hour cycle have different timekeeping issues: one gains 2 minutes daily while the other loses 3 minutes. To determine when they will next show the correct time together, calculations reveal that Watch 1 takes 360 days to reset, and Watch 2 takes 240 days. The least common multiple (LCM) of these two periods is 720 days. Therefore, both watches will next display the correct time together after 720 days. The solution is confirmed as correct.
Marcelo Arevalo
Messages
39
Reaction score
0
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.
 
Mathematics news on Phys.org
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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top