When taking a shower, the water comes from the shower head and the faucet in the tub. Then the tub drains really slow. How can we fix this problem, we wait about 15-25 minutes before the person can shower.

Your diverter is not holding. Either replace the diverter or clean it out. The drain likely has a hair or soap buildup. Remove the drain cap and pick the hair out with a coathanger made into a small hook to twirl the hair like spaghetti and remove it. You may have a lever tub drain that also may need adjustment.