My math professor loves to give us word problems. Applications of mathematical concepts to real-life, every day scenarios. And that's great! Learning how to apply math that you learn to the real world is important - it's why math was created in the first place.
Trouble is, he likes boats that go up and down stream. And every time I see one now, I flinch.
The first time we saw a boat problem in the context of a linear systems exam to find the speed of a boat in still water, and the speed of the current. The exam was very helpful, and gave us several pieces of information - like how long it took upstream and downstream. But I'd never seen this sort of problem before. So I looked at the exam paper, and looked around the room. Everyone else was writing furiously, with steam rising from their ears. It was a pretty bad exam. I started trying to remember my high school physics, and wondered how the viscosity of water and drag from any wind might start affecting the wind speed, and by the time the exam was over ended up gloriously confused.
So, today, we had a different problem. A boat traveling at a speed in water, goes upstream and downstream in 1 hour and 4 minutes. They travel 6 kilometers upstream and return, and the boat is going at 12 miles per hour. Find the speed of the current!
R*T=D problems were always my favourite in physics, not so much in algebra. Mainly because when it comes to setting up my grid:
| Direction | Rate | Time | Distance |
| Upstream |
 |
 |
6 km |
| Downstream |
 |
 |
6km |
I always get confused as to which way is up, and which way is down! Of course, it doesn't actually matter in the end since, as long as you're consistent, you'll end up in the same place. But still. The trick, I've found, is to not get bogged down by weird numbers. Sometimes you end up with horrible rates, and long, complex, quadratic equations. It usually simplifies out in the end.
The above problem was on my last exam, by the way. It was horrible until the last quarter of it when I suddenly went: "omg thats it!" - those moments are awesome. And, boats can't travel negative speeds. But you end up with two answers. You can throw the negative answer away, unless you happen to have a Delorian attached to the boat.
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