It just interchanged, check this out man
Algebra
Level
pending
A dog left his home at past 3:00 o'clock P.M. as indicated in his wall clock. between two to three hours after, he returned home and noticed that the hands of the clock interchanged. At what time did the dog leave his home?
3:32.47
3:30.47
3:33.47
3:31.47
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1 solution
The minute-hand leaves the 0:30 mark at 3:30, traveling one tick per minute. We affix the hour-hand of another clock at 6:00 exactly and start it off at the same time, also traveling 1 tick per minute. This will send the 2nd minute-hand coursing along at 12 ticks per minute from the :00 mark. We have a 3rd clock start at 12:00, its hour hand moving at 12 ticks per minute. Its minute hand will speed around at 12*12=144 ticks per minute. When the time on the third clock matches the time on the first clock exactly, that will be our answer.
3.5 + (1/60 t) = (144/60 t)
This should give us the exact minutes in decimal form past 3:30
3.5 = 143/60 t
t = 210/143 ≈ 1.47
3:30 + 210/143 ≈ 3:31.47