A boy leaves home in the morning to go to school. At the moment he leaves the house he looks at the clock in the mirror. The clock has no number indication and for this reason the boy makes a mistake in interpreting the time (mirror-image). Just assuming the clock must be out of order, the boy cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is two and a half hours later than the time that the boy saw on the clock at home.
At what time did he reach school?

The boy left home at 7:05. He thought it was 4:55. he arrived at school at 7:25, 20 minutes after 7:05 and 150 minutes after 4:55

The time that the boy left was h1:m1 that is h1 hours and m1 minutes after midnight.

The time he thought it was was h2:m2

The time he arrived at school was h3:m3

h2 = 1-h1 (mod 12) => h1 + h2 =11 [For example, If the hour hand was between 3 and 4, the boy thought it was between 8 and 9 and h1 = 3, h2 = 8]

m2 = -m1 (mod 60) => m1 + m2 =60

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60h1 + m1 + 20 = 60h3 + m3

60h2 m2 + 150 = 60h3 + m3 = 60h1 + m1 + 20

60(h1-h2) + (m1-m2) = 130
60(2h1-11) + (2m1-60) = 130
120h1 - 660 + 2
120h1 + 2m1 - 720 = 130
120h1 + 2m1 = 850

0<2m1≤120 and h1 is an integer, so 120h1 must be a multiple of 120

850 = 840 + 10 is the only way to satisfy these conditions, so m1 = 5 and 120h1 = 840 => h1 = 7

Edited on February 7, 2004, 11:03 am

Posted by TomM on 2004-02-07 11:00:33