SOLUTION: 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 looke

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(52752) (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?
~~~~~~~~~~~~~~~~

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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