Sounds like interval arithmetic:

use List::Util qw( min max );
sub overlap {
  my @intervals = @_[0, 1];
  my $left  = max( map $_->[ 0 ], @intervals );
  my $right = min( map $_->[ 1 ], @intervals );
  return max( 0, $right - $left );
}
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Just turn the 3rd and 4th args to seconds relative to the epoch, and use the above function, with the intervals passed as array refs [ $time1a, $time1b ], [ $time2a, $time2b ].