I think you could also take a bit of sharpened pipe and push it through the middle to core the apples, too. You could be peeling while your twin could be coring.
+Dave Schuetrum I have an apple corer that is something like what you describe but it does not work very well. I core the apples in the traditional way by quartering and then cutting out the core.
+Dave Schuetrum Using an apple corer is faster even though it sometimes misses part of the core. The main thing I do not like about using an apple corer is that they waste some of the apple.