A: "The time now equals quarter of the time that passed since noon till now plus half of the time left from now till tomorrow's noon."

Please express R's response in HH:MM format.

Abridged from Dudeney's " Amusements in Mathematics" (1917)

There are two possible solutions to the problem.

If the current time is in the afternoon, then the time is 9:36 pm.

(noon < now < midnight < noon of the day following now)
T = T/4 + (24 - T)/2
5T = 48
T = 48/5 = 9 3/5 = 9 hours 36 minutes after noon

If the current time is in the morning then the time is 7:12 am.

(noon < midnight < now < noon < noon of the day following now).
(12+T) = (12+T)/4 + (48 - (12+T))/2
5T = 36
T = 36/5 = 7 1/5 = 7 hours 12 minutes after midnight

Posted by Dej Mar on 2011-09-19 22:35:35