Is there a faster way to delete orphaned table entries - php

Question

I currently have 20,000 rows in the listing table, and already this query is running quite slow.
What it does is delete all listing rows where the current time is 60 seconds or more since the listing endDate and where the listing is not associated with any task.
DELETE
listing
FROM
listing
LEFT JOIN
task
ON
task.listingId = listing.listingId
WHERE
task.listingId IS NULL
AND listing.endDate < DATE_SUB(NOW(), INTERVAL 1 MINUTE)
Is there a faster way to delete the orphaned listing rows?
UPDATE:
The original (above) query takes 11.6 secs.
This equivalent bunch of queries takes 0.09 secs, but it's a lot messier and requires a bunch of PHP:
$q = "
SELECT
listingId
FROM
task
";
$result = mysql_query($q) or die(mysql_error());
$taskListingIds = array();
while ($task = mysql_fetch_array($result)) {
$taskListingIds[$task['listingId']] = NULL;
}
$q = "
SELECT
listingId
FROM
listing
WHERE
endDate < DATE_SUB(NOW(), INTERVAL 1 MINUTE)
";
$result = mysql_query($q) or die(mysql_error());
while ($listing = mysql_fetch_array($result)) {
if (!array_key_exists($listing['listingId'], $taskListingIds)) {
$q = "
DELETE
FROM
listings
WHERE
listingId = " . $listing['listingId'] . "
";
mysql_query($q) or die(mysql_error());
}
}
I'll stick with this for now, but any suggestions for a fast way to do this purely with SQL would be great.