"thinking clearly" "string puzzle" symbolic algebra calculator

I gave my two boys an old puzzle to solve yesterday. I told them that I’d give them each $10 if they could solve it for me. It’s one of the ways we do the “allowance” thing around the house sometimes.

Here’s the puzzle. A piece of string is stretched tightly around the Earth along its equator. Imagine that this string along the equator forms a perfect circle, and imagine that to reach around that perfect circle, the string has to be exactly 25,000 miles long. Now imagine that you wanted to suspend this string 4 inches above the surface of the Earth, all the way around it. How much longer would the string have to be do do this?