Aggregating document list by score

[API_PHP]

I have 3 arrays, each containing a dynamically generated list of documents. (The list changes depending on what the user searches for)

    $list1['documentname']
    $list2['documentname']
    $list3['documentname']

Each array is multidimensional and contains other information such as description. 

$list1 = array('documentname','description') 

For example if I wanted to output the sixth document`s name and description I would write: 

echo $list1[5]['documentname'].$newline.$list1[5]['description'];

A particular document may be contained in all three lists or none of the lists. What I am trying to do is rank the documents by the documents total score using the following formula:

    $document_Score = (1/(60+rank_list1)) + (1/(60+rank_list2)) + (1/(60+rank_list3))

I am trying to think of a way of doing this but I am getting nowhere.  

 

If document a is ranked 1 in list1, 2 in list2, and 4 in list3, how do I apply the following formula and add the scores together. 

    $document_Score = (1/(60+1)) + (1/(60+2)) + (1/(60+4)) //score for document a

I know that I need to apply code based on whether $list1['documentname'] is equal to $list2['documentname'] etc but I have no idea how to implement this. Any tips or ideas would be appreciated.

 

Any ideas?

 

Thanks.