I have A JD JX75 push mower that when you engage the mower the blade will not engage right away. It may take 10 or 20 seconds

Hi,
Most probably the liner in the BBC has broken off and the pieces have been ejected. Usually this is accompanied with a metal-on-metal grating sound during engagement and sometimes with the blade stopping in high grass.
There are two versions of that machine with different engines. Up to serial number 200000 it uses an FC150V engine and a GC90029 clutch. Replacement is your option there. Starting with serial number 200001 it had a FJ180V engine and a GY20805 clutch. The bottom portion of that was separately replaceable with a GY20711, though it is seldom wise or a good fix except as a warranty part.
The serial number of the machine is built into the model number on the tag on the rear of the machine. It should start GXJX75, have a letter of the alphabet as a separator/ designator and then a six digit number that is the serial number I just used in my description.
Peace,
Clarke