How many mph would you be going when you came out the other side if you fell in a whole that went all the way through the earth?

You wouldn't. Aside from the fact that you would burn up as you reached the earths core, you have to think of gravity.If you have a hole on one side of the earth and you fall in it you would fall to the center of the earth. If there was a hole on the exact opposite side of the earth and the fellow over there fell into it he would fall toward the center of the earth. If both holes went to the center of the earth and were joined, and molten magma didn't come out, then I would reason that you would fall no further than the center.