2 Clocks Time Difference

Question

Two clocks are set at the ch time will they show a difference of 15 minutes?same time; one is seen to gain 40 seconds and other to lose 50 seconds in 24 hours. In how mu

Answer 1

First, try to picture two clocks.  They are 12-hour analog (not digital) clocks with only 12 hours represented (not 24 hours or a.m./p.m.), so we are only looking for the first 15-minute difference in times shown.  There is an hour-hand and a minute-hand; the 15-minute difference between clocks involves both hands, not just one.

Second, realize that actual time only matters at the start.  The two clocks are inaccurate after that.  It is their difference (not the actual time) that is important.  The problem asks “in how much time,” which means elapsed time from the start.

 

The math –

 

The total difference in the times shown at the end is:

     15 minutes = 15*60 seconds = 900 seconds.

 

In a 24-hour period,  one clock gains 40 seconds and the other clock loses 50 seconds, so they show times that are 90 seconds different [40 - (-50)] at the end of the first day.

 

In order to show times that are 900 seconds different, the clocks must run:

     900/90 = 10 periods of 24-hours = 10 days