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Algebra teachers must love trains - it seems that a lot of algebra questions involve train travel, with trains on different tracks.

Let's start with the most simple of train problems. Both trains start at the exact same spot, on tracks that run side by side. Both start at the exact same time, both heading north. One has a big engine and can run at 60 mph. The other train is a smaller train and can only run at 45 mph. When the big train has gone 120 miles, how far has the smaller train gone?

The first thing to do when looking at a word problem is look for numbers. Those are the important parts. We have 3 numbers here: 60, 45, and 120. Two of those numbers are for similar things. 60 is Train #1 speed, and 45 is Train #2 speed. On the other hand, we have 120 for Train #1 distance and ??? for Train #2 distance. So we'll call Train #2's distance "X".

We know both trains ran for the same amount of time, and we know how fast they were going, and we know how far one train got in that time. So we should be able to determine how far the other train got, too. The proportion of Train #1's speed over Train #2's speed will be the same as the proportion of Train #1's distance over Train #2's distance.

60 = 120
--- ----
45 X

To solve a problem like this, you multiply the top left with the bottom right, and it will equal what you get when you multiply the bottom left with the top right. So you do:

60X = 45 * 120

so

60X = 5400

Now if you divide both sides by 60, X will be left alone on the left side. So that equals

X = 90

So the answer is that Train #2 went 90 miles during this time.

Try some of the practice examples to get the hang of it!