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 May 1st, 2019, 11:26 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 354 Thanks: 1 How to solve this fast and slow clock problem? At 3:00 pm, clock was showing regular time. There are two clocks, one gains 5 min per hour. Another one loses 5 mins per hour. After how many hours both clocks will show the same time again?
 May 2nd, 2019, 04:45 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,623 Thanks: 2076 Do the two clocks show whether the time is am or pm?
May 3rd, 2019, 03:10 AM   #3
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Quote:
 Originally Posted by skipjack Do the two clocks show whether the time is am or pm?
YES. But how to solve the problem?

 May 3rd, 2019, 05:45 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,623 Thanks: 2076 If the clocks show the same time initially, they'll next do that when they're out of step with each other by 24 hours (because they don't show the date). They get out of step with each other by 10 minutes every hour, so this will take 144 hours (because 1440 minutes is 24 hours).
May 8th, 2019, 08:10 AM   #5
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Quote:
 Originally Posted by skipjack If the clocks show the same time initially, they'll next do that when they're out of step with each other by 24 hours (because they don't show the date). They get out of step with each other by 10 minutes every hour, so this will take 144 hours (because 1440 minutes is 24 hours).
Answer is 72 hours, I don't know how to do it?

 May 8th, 2019, 06:06 PM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024
 May 8th, 2019, 11:07 PM #7 Senior Member   Joined: Aug 2014 From: India Posts: 354 Thanks: 1 Each hour clock A runs 5 minutes fast, after 12 hours, clock A is indicating 1 hour later than it should be. Although it is 3, it shows 4. Similarly, because each hour clock B runs 5 minutes slow, after 12 hours, clock B is indicating 1 hour earlier than it should be. Although it is 3, it shows 2. At t = 0h: Clock A points to 3. Clock B points to 3. At t = 12h: Clock A points to 4. Clock B points to 2. At t = 24h: Clock A points to 5. Clock B points to 1. At t = 36h: Clock A points to 6. Clock B points to 12. At t = 48h: Clock A points to 7. Clock B points to 11. At t = 60h: Clock A points to 8. Clock B points to 10. At t = 72h: Clock A points to 9. Clock B points to 9.
 May 9th, 2019, 05:48 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,623 Thanks: 2076 The times (after 72 hours) wouldn't match, as one would be 9 pm and the other 9 am.

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