Hard to say without a Whirlpool Model Number.
You could try going to the Whirlpool site and see if there is a unit which looks the same as yours then use that as a Model Number.

Take a look in your manual and try to find out what is happening at that time during the cycle.
For instance it may be waiting for the water to warm up to a certain temperature. If the heater is shot then it will hang the cycle.