SOLUTION: A clock is 4 minutes slower than normal time per hour. You set it to be accurate at 8 AM. When this clock hits 12 at noon exactly, what time is it?

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Question 1163944: A clock is 4 minutes slower than normal time per hour. You set it to be accurate at 8 AM. When this clock hits 12 at noon exactly, what time is it?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let t%5Bs%5D be the reading of the slower clock;  t be the normal clock reading (= actual time).


Then from the condition  %28t%5Bs%5D+-+8%29%2F%28t-8%29 = %2860-4%29%2F60 = 56%2F60 = 14%2F15  for any time interval t after 8:00 am.


When this clock hits 12 at noon exactly, t%5Bs%5D-8 = 4;  hense


    4%2F%28t-8%29 = 56%2F60,  or


    4%2F%28%2856%2F60%29%29 = t - 8

    %284%2A60%29%2F56 = t-8

    60%2F14 = t -8

    t-8 = 4 hours + 4%2F14 of an hour = 4 hours and 0.286 of an hour = 4 hours 17 minutes and 9.6 seconds.


ANSWER.  At this moment, the correct time is  17 minutes and 9.6 seconds after noon.

Solved.