while (mysql_fetch_array) in a while loop

What you are doing there is bad on multiple levels. And your english horrid. Well .. practice makes perfect. You could try joining ##php chat room on FreeNode server. That would improve both your english and php skills .. it sure helped me a lot. Anyway ..

The SQL

First of all, to use ORDER BY RAND() is extremely ignorant (at best). As your tables begin the get larger, this operation will make your queries slower. It has n * log2(n) complexity, which means that selecting querying table with 1000 entries will take ~3000 times longer then querying table with 10 entries.

To learn more about it , you should read this blog post, but as for your current queries , the solution would look like:

SELECT duration 
FROM table 
    JOIN (SELECT CEIL(RAND()*(SELECT MAX(id) FROM table)) AS id) as choice
WHERE 
    table.id >= choice.id
    rank = 1 
LIMIT 1

This would select random duration from the table.

But since you you are actually selecting data with 3 different ranks ( 1, 2 and 3 ), it would make sense to create a UNION of three queries :

SELECT duration 
FROM table 
    JOIN (SELECT CEIL(RAND()*(SELECT MAX(id) FROM table)) AS id) as choice
WHERE 
    table.id >= choice.id
    rank = 1 
LIMIT 1
UNION ALL
SELECT duration 
FROM table 
    JOIN (SELECT CEIL(RAND()*(SELECT MAX(id) FROM table)) AS id) as choice
WHERE 
    table.id >= choice.id
    rank = 2 
LIMIT 1
UNION ALL
SELECT duration 
FROM table 
    JOIN (SELECT CEIL(RAND()*(SELECT MAX(id) FROM table)) AS id) as choice
WHERE 
    table.id >= choice.id
    rank = 3 
LIMIT 1

Look scary, but it actually will be faster then what you are currently using, and the result will be three entries from duration column.

PHP with SQL

1. You are still using the old mysql_* functions to access database. This form of API is more then 10 years old and should not be used, when writing new code. The old functions are not maintained (fixed and/or improved ) anymore and even community has begun the process of deprecating said functions.

   Instead you should be using either PDO or MySQLi. Which one to use depends on your personal preferences and what is actually available to you. I prefer PDO (because of named parameters and support for other RDBMS), but that's somewhat subjective choice.

2. Other issue with you php/mysql code is that you seem to pointlessly loop thought items. Your queries have LIMIT 1, which means that there will be only one row. No point in making a loop.

3. There is potential for endless loop if maximum value for duration is 1. At the start of loop you will have $sum === 15 which fits the first while condition. And at the end that loop you can have $sum === 18 , which satisfies the second loop condition ... and then it is off to the infinity and your SQL server chokes.

And if you are using fractions for duration, then the total value of 3 new results needs to be even smaller. Just over 2. Start with 15.99 , ends with 18.01 (that's additional 2.02 in duration or less the 0.7 per each). Again .. endless loop.

Suggestion

Here is how i would do it:

$pdo = new PDO('mysql:dbname=my_db;host=localhost', 'username', 'password');
$pdo->setAttribute(PDO::ATTR_EMULATE_PREPARES, false);
$sum = 0;
while ( $sum < 16 )
{
    $query = 'that LARGE query above';
    $statement = $pdo->prepare( $query );
    if ( $statement->execute() )
    {
        $data = $statement->fetchAll( PDO::FETCH_ASSOC );
        $sum += $data[0]['duration']+$data[1]['duration']+$data[2]['duration'];
    }
}
echo $data[0]['duration'];

This should do what your code did .. or at least, what i assume, was your intentions.