Here is, I believe, a great math question for any kids in grades 8 or above...in case you have to ever prove the relevance of math to your kids.
So I had a great time today out at my beloved camp on a remote lake in New Hampshire. Unfortunately, the pump in my septic system burned out so I had to get the guys out to replace it. I was there, of course, to oversee the process.
It turned out that because of the tendency towards freezing temperatures in this area, the piping that goes from the septic pump to my leach field would empty back into my pump tank once the pump shut off (which it does automatically, through a float mechanism). Since the leach field is 100 yard from the tank, this is potentially a lot of liquid coming back into the tank after the pump shuts off. One could envision a situation where the pump would be on more or less continuously: the tank would fill, the pump would turn on from a float mechanism, it would pump until the level in the tank went down to a certain point and then shut off, all the liquid in the 100 yards of 2 inch piping would run back into the tank, at which point the pump would turn back on....You can imagine the electricity bill from this endless do-loop, as well as imagine how long the new pump would last under such circumstances.
So two math questions emerged. How much liquid will 100 yards of 2 inch piping hold? (Let's assume that the 2 inches is the internal diameter, not external.) Two, what is the capacity of a pump tank that is 4 feet in diameter and 5 feet tall? And last, if the pump turns off and on in a range of 2 feet vertically, how much liquid will be pumped out in one pumping?
All this should help us figure out if the back draining of the water in the pipe will simply fill the tank enough to turn the pump back on, or if that is an issue we can ignore and go to sleep.
Good math stuff. What I haven't gotten into is the really interesting thing, which is how we used a little logic and a little knowledge of electrical circuits to figure out that there has to be a short somewhere between the house and the pump. Now I get to dig up the cable and find if our theory is true! Ah, the pursuit of truth! I love it.