The pace of Jim's watch is slower by 3 minutes in comparison with Kim's watch for every one hour. The difference increases as the hours pass by.
The time and "am" and "pm" of the watch coincide when the difference between the two clocks reduces to 24 hours. The two clocks display the same time including am and pm.
For a difference of 24 hours, the clock needs to lag by
1440minutes.
For every one hour, the clock lags by 3 minutes. Hence in order to have a difference of
1440minutes, it takes
=480hours . This is equivalent to 20 days of time.
Hence for every twenty days, they display the same time.
In the period of Jan 1 and June 1, there are 150 days which includes 720 day intervals. Along with the 7 times once on Jan 1st and once on June 1st, they display the same time.
A total of 9 times.