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Question 1192359: There are two clocks in my house. One clock gains one minute every minute and the other loses two minutes every hour. Yesterday I set them both to the correct time but when I looked at them today, I saw that the time shown on one was 11:00 and shown on the other was 12:00. What time was it when I set the two clocks?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
I think it can safely be assumed that the statement of the problem is supposed to say the clock that runs fast gains one minute every hour -- not one minute every minute.
The times shown on the two clocks diverge at a rate of 1+2=3 minutes every hour.
For them to show times that differ by 1 hour (60 minutes), they must have been running for 60/3=20 hours after they were set.
In 20 hours, the clock that gains 1 minute each hour will show a time change of 20 hours and 20 minutes. It now shows a time of 12:00; 20 hours and 20 minutes before 12:00 is 20 minutes before 4:00, or 3:40.
OR....
In 20 hours, the clock that loses 2 minutes each hour will show a time change of 40 minutes less than 20 hours, or 19 hours and 20 minutes. It now shows a time of 11:00; 19 hours and 20 minutes before 11:00 is 20 minutes before 4:00, or 3:40.
ANSWER: The two clocks were set at 3:40.
Answer by ikleyn(52751)  (Show Source):
You can put this solution on YOUR website! .
There are two clocks in my house. One clock gains one minute every minute and the other loses two minutes every hour.
Yesterday I set them both to the correct time but when I looked at them today, I saw that the time shown on one was 11:00
and shown on the other was 12:00. What time was it when I set the two clocks?
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Notice that the solution by @greenestamps is not consistent with the problem's formulation.
It is very possible, that the problem's formulation is incorrect and should be fixed - - - then it deserves to be noticed, at least.
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