What do the leaves and stems of the plant look like? Did you spray the plant with fungicides at all?

It is best to post a picture because it is hard to know without seeing the plant.

red on the bottom with black patches towards the top

Are the black patches like the dark, greenish-brown areas on the shoulders of some "black" tomato varieties? If so, your Park's Whopper may be a different variety. [This year my 17 purchased seedlings include at least one, possibly two mis-labelled varieties.]
http://heirloomtomatoplants.com/The%20Black%20Tomatoes.htm

Or do you mean black patches that might be mold or decay in the cracks?

Or something else?

Here are some photos of problems that affect tomato fruit:
http://vegetablemdonline.ppath.cornell.edu/DiagnosticKeys/TomFrt/TomFrtKey.html
http://aggie-horticulture.tamu.edu/publications/tomatoproblemsolver/ripe/

Thank you for responding so quickly! Unfortunately I do not have a camera therefore I cannot take a picture of it. But based upon the links my problem is most likely early blight. The black patches on my fruit match the picture in the other link. I sprayed last week with a fungicide and I thought it was working but it didn't. My other tomato varieties remain good though. What should I use to prevent it from spreading farther? What do you recommend?