Going with your original idea, I came up with this:

open my $pstat, "<", "/proc/$ARGV[0]/stat" or die "$!";
chomp(my $stat_line = <$procstat>);
close $pstat;

my $time_offset = (split / /, $stat_line)[21];
$time_offset = int $time_offset / 100;

my $btime;
open my $stat, "<", "/proc/stat" or die "$!";
while (<$stat>) {
  if (/^btime (\d*)/) {
    $btime = $1;
    last;
  }
}
close $stat;

my $start_time = $time_offset + $btime;
my $length = time - $start_time;
print $length;
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FYI, a jiffy is the time for one tick of the system interrupt timer, which happens to be 100Hz on my computer. That means this code is not portable. It would be if I knew a way to get the interrupt period at run time.