Two joggers each run at their own constant speed and in opposite directions from each other around an oval track. They meet every 36 seconds. The first jogger completes one lap of the track in a time that, when measured in seconds, is a number (not necessarily an integer) between 80 and 100. The second jogger completes one lap in a time, t seconds, where t is a positive integer. What is the product of the smallest and largest possible values of t?