The was nothing requiring date math in the OP, but DateTime also does time math. Since the OP is dealing with durations, she'd need DateTime::Duration.

Unfortunately, it doesn't produce the result one would expect because DateTime(::Duration) realises that not every minute has 60 seconds. Some are longer due to leap seconds.

use strict;
use warnings;

use DateTime::Duration qw( );

my @times = qw( 5:21 8:01 5:37 7:19 5:46 7:44 6:43 7:17 8:02 6:50 7:54
+ 8:44 );

my $dur = DateTime::Duration->new();
for my $time (@times) {
   my ($mins, $secs) = split(/:/, $time);
   $dur += DateTime::Duration->new(
      minutes => $mins,
      seconds => $secs,
   );
}

printf("%s hours, %s minutes, %s seconds\n",
   $dur->in_units(qw( hours minutes seconds ))
);
[download]

1 hours, 19 minutes, 378 seconds
[download]

From the docs, the only conversions possible are:

• years ⇔ months
• weeks ⇔ days
• hours ⇔ minutes
• seconds ⇔ nanoseconds

Now, you can use a reference datetime to determine minute length.

...

my $dur2 = do {
   my $ref = DateTime->new(
      year => 2006, month => 1, day => 1,
      hour => 0, minute => 0, second => 0,
      time_zone => 'UTC',
   );
   $ref + $dur - $ref
};

printf("%s hours, %s minutes, %s seconds\n",
   $dur2->in_units(qw( hours minutes seconds ))
);

my $dur3 = do {
   my $ref = DateTime->new(
      year => 2005, month => 12, day => 31,
      hour => 23, minute => 59, second => 59,
      time_zone => 'UTC',
   );
   $ref + $dur - $ref
};

printf("%s hours, %s minutes, %s seconds\n",
   $dur3->in_units(qw( hours minutes seconds ))
);
[download]

1 hours, 19 minutes, 378 seconds
1 hours, 25 minutes, 18 seconds   # All of the minutes had 60 seconds.
1 hours, 25 minutes, 19 seconds   # One of the minutes had 61 seconds.
[download]

Update: Added example where leap seconds affect the result.

Unfortunately, it doesn't produce the result one would expect because DateTime(::Duration) realises that not every minute has 60 seconds. Some are longer due to leap seconds.

From the docs, the only conversions possible are:

• years ⇔ months
• weeks ⇔ days
• hours ⇔ minutes
• seconds ⇔ nanoseconds

Ah, so, Date::Time favours geek correctness over usability. And by doing so, it's not POSIX compliant (as POSIX says leap seconds are to be ignored). While taking care of leap seconds is useful in some cases, stubbornly refusing to do second/minute conversion because of a leap second every few years most of society ignores without problems makes the module far less useful than it could be.

Ah, so, Date::Time favours geek correctness over usability.

First, it's DateTime, not Date::Time. The purpose of the module is to manipulate date-times, not time durations. DateTime::Duration is a helper object to help DateTime do date arithmetic. It's not designed to contain a result.

When using the module as intended, it provides both a correct mode and a lax mode (the 'floating' time zone) for usability, so your claim is false.