The Man and the Dog

A Classic Puzzle by Henry Ernest Dudeney
Yes, when I take my dog for a walk, said a mathematical friend, he frequently supplies me with some interesting puzzle to solve. One day, for example, he waited, as I left the door, to see which way I should go, and when I started he raced along to the end of the road, immediately returning to me; again racing to the end of the road and again returning. He did this four times in all, at a uniform speed, and then ran at my side the remaining distance, which according to my paces measured 27 yards. I afterwards measured the distance from my door to the end of the road and found it to be 625 feet. Now, if I walk 4 miles per hour, what is the speed of my dog when racing to and fro?

This one can be done by quite standard algebra which needn't be belabored here. The answer is of course on the order of 10^24 angstroms per epoch, or 16 miles per hour.