Translating a Word Problem into a System of Equations Examples

Set up a system of equations describing the following word problem:

Whenever Anna drives, she goes one speed. Whenever Bob drives, he drives one speed. Anna and Bob went on a road trip together. They insist it's strictly platonic, but that goo-goo-ga-ga look in their eyes says differently.

The first day Anna drove for 2 hours, Bob drove for 3 hours, and they went 340 miles. The second day Anna drove 4 hours, Bob drove 1 hour, and they went 330 miles. How fast does Anna drive? How fast does Bob drive? Will they or won't they?

The unknown quantities are Anna's speed and Bob's speed. We can tell this from the first and last parts of the problem. The problem says

"Whenever Anna drives, she goes one speed."

If we weren't going to be asked to find Anna's speed, the problem could have just told us how fast she drives, and if the problem wasn't dead set on being sneaky, it would have. Also, towards the end of the problem, it asks

"How fast does Anna drive?"

That's almost screaming out "Anna's speed is an unknown quantity that we want to find!" Once again, a problem is screaming something out when it could have just as easily gotten the information across by speaking in a calm, controlled manner.

Let's say x is Anna's speed, and y is Bob's speed.

Now we need the two pieces of actual information that are given to us. In this problem, the first piece of information is what happened on the first day. If Anna drove for 2 hours and Bob drove for 3, then the two traveled

2x + 3y miles.

Our first equation is therefore

2x + 3y = 340.

The second piece of information is what happened on the second day: Anna drove 4 hours and Bob drove 1, and they went 450 miles, so

4x + y = 330.

If x is Anna's speed and y is Bob's speed, then the problem is described by the system of equations