Your 64bit OS is designed to run both 32 & 64 bit applications; that is perfectly normal. Your system, for example, has both IE-32bit and IE-64bit but because add-ins are limited for 64bit, the IE 32bit browser is the default.
If your computer is slow it could be a virus, or heavy processing, or an automatic update running, or it could even be your anti-virus software. I think you need to do a little more checking, don't assume it is because you happen to have a 32-bit app running.
I suggest you install Process Explorer and keep it in a window you can watch while you perform other tasks and see what is using your CPU when your system slows. Links to Process Explorer can be found
HERE.