suppose we have two clock A and B. each hour A clock outruns by 2 minute then B which always shows correct time.in 1 January both clock was corrected and it was showed 16:00 question is what what will be first time when both o'clock will show again the same time?there is list of answers from which correct one is 16 January 16:00 please can anybody explain me why?
[Math] Clock A gains $2$ minutes per hour over clock B; when do they next show the same time
algebra-precalculus
Best Answer
If the two clock show the same time of day (in a 24-hour sense, since you've said 16:00), then clock A has gained some multiple of 24 hours on clock B. Since clock A gains 2 minutes per hour, gaining 24 hours = 1440 minutes takes 720 hours, which is 30 days, exactly...
Okay, backing up, let's suppose we're talking 12-hour clocks, so they match up when A has gained 12 hours = 720 minutes, which takes 360 hours, which is exactly 15 days. So, 15 days from 16:00 Jan 1 is 16:00 Jan 16, at which time clock B will correctly show 16:00 Jan 16 and clock A will show 04:00 Jan 17, so both will show "4 o'clock."