A perfect number is a number which is equal to the sum of all its divisors. For example 6 is divisable by 1,2,3 and 1 + 2 + 3 = 6. Can you find another perfect number?

Matthew 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, Matthew 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 Matthew saw on the clock at home.

At what time did he reach school?

A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mph faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?