35th Swedish 1995 Problem 2 X left home between 4 and 5 and returned between 5 and 6 to find that the hands of his clock had changed places. What time did he leave?
26 122/143 minutes after 4 Solution When he returns the hour hand is between 5 and 6, so the minute hand must have been between 5 and 6 when he left. So he left at 4 hours (25+x) minutes for some 0 ≤ x ≤ 5. That is (25+x)/60 hours after 4, so the hour hand must have been at 20 + (25+x)/12 minutes. When he got back the minute hand is at 20+(25+x)/12, so it is (20+(25+x)/12)/60 hours after 5, so the hour hand must be at 25 + (20+(25+x)/12)/12 minutes. Hence 12x = 20+(25+x)/12, so 144x = 240 + 25 + x, x = 265/143 = 1 122/143. 35th Swedish 1995 © John Scholes jscholes@kalva.demon.co.uk 16 January 2004 Last corrected/updated 16 Jan 04