# Like Ripkin

I haven’t been sleeping well so I was almost relieved when I got back to my CHU after teaching math for two hours at the end of the day to find that the Internet had gone down and I wouldn’t have to make a post. Then of course nature kicked in and I had to fiddle with it until it started working again.

The math class had an interesting problem on some of the homework I had assigned. I knew how to figure it out using a brute force-like approach but I stumbled for a good ten or fifteen minutes trying to figure out an elegant way to explain the problem: something simple enough to be understood while providing a good foundation for future reasoning, rather than a simple trick based on memorization or a pseudo-formula magic incantation. The problem was “If it takes 5 men working 4 days to load 5000 tons, how long does it take 8 men to load 10,000 tons?”

Well, the elegant way is to figure it takes one man four days to load 1000 tons, or “1000 tons per man per 4 days” which is trivially rewritten as “250 tons per man per day.” Now, you multiply the whole thing by 8 men: 2000 tons per day. Then 10,000 tons divided by 2000 tons/day is (10,000 tons/2000 tons) * 1 day, or 5 days. It looks a lot better written out because you can see the units build up and then cancel out, which is how you know you have the right answer. The units in this case are: tons, days, and men.