What you have here is an array of hashes; that is, each element of your array is a hash (a structure containing elements, each of which is identified by a key).
In order to add a key and value, you just assign it, like this:
$array[0]["distance"]=100;
$array[1]["distance"]=300;
#and so on
PHP hashes and arrays in general are documented here.
Now, in order to sort your array (each of whose elements is a hash), you need to use the "uasort" function, which allows you to define a comparison function; in this comparison function you define the behavior you want, which is sorting on the value of the distance key.
Something like this:
// Comparison function, this compares the value of the "distance" key
// for each of the two elements being compared.
function cmp($a, $b) {
if ($a["distance"] == $b["distance"]) {
return 0;
}
return ($a["distance"] < $b["distance"]) ? -1 : 1;
}
Once this is defined, you call uasort like this:
uasort($array, 'cmp');
Find more documentation on uasort here.