1986 Toyota Corolla whenever it rains, the car doesn't run

1986 Toyota Corolla mileage: 175,000. I recently bought this car and whenever it rains, the car doesn't run once I have been driving for about ten minutes. It runs fine after I add a can of dry gas. I was wondering if I have a hole in my gas tank. Someone had told me that it might be the distributor cap, but since the dry gas helps I don't think that is the problem. Will the dry gas damage my engine?