I assume what you mean is that the drainpipe coming out of the washing machine is going into a 1 1/2 inch pipe in the wall. Whether that is a big enough pipe depends on the volume of water coming out of the machine, and whether the lint in the water coming out of the machine clogs that pipe. With an older house, the pipes were generally built to handle a smaller top-loading washer, which was standard at that time. However, bigger top loading machines may make a larger volume of water than the pipe was designed to carry. However, a front-loading high-efficiency machine doesn't use as much water and may work fine unless the lint clogs the pipe.