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Answer :
The correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.
Call the clock that runs forward A and the clock that runs backward B. Clock A will display the time as 13:00 at that moment, but clock B (which is going backward from 13:00) will display the time as 11:00.
Clock A will move two hours on its display in one hour since it is operating at twice the typical speed. Clock A will display 15:00 an hour from now, at 14:00. Additionally, because clock B is going backward, its display will read 10:00 an hour from now.
The clocks will next sync up when Clock A displays 13:00 (its initial beginning time) and Clock B displays 11:00, which takes place after 12 hours (12 hours on clock A, 24 hours on clock B).
So the correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.
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