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my $day1_prog1_start = Date_to_Time(2007, 8,  8, 17, 0, 0);
my $day1_prog2_start = Date_to_Time(2007, 8,  8, 23, 0, 0);
...

print("If Prog1 starts at $next_prog1_start_str,\n");
print("Prog2 will likely start at $next_prog2_start_str.\n");

Prog2 usually starts 10800 seconds after Prog1 start.
If Prog1 starts at 2007/08/09 22:00:00,
Prog2 will likely start at 2007/08/10 01:00:00.