The equation for the 2nd train is 30x-40 because it is traveling 30 mph and started when the other train was 40 miles away.

You want to know when they are at the same location so you set them equal to each other.

20x = 30x-40

when you solve you get that x=4

They are at the same location in 4 hours or 80 miles away.

20 *4 = 80

30*4 – 40 = 80

Hope this helps.

Rousey

Train 1 will have traveled 20(h+2) miles and train 2 will have traveled 30h miles. Set the distances equal and solve for h.

That is big idea number one.

Big idea number two is to figure out if they are heading in the same direction or not. In this case, they are, and one has a head start. So in problems like these, their distances will be the same, and you have to set each of them equal to one another. But it is not distance=distance, it is rate times time (equals) rate times time.

Big idea number three comes with practice. YOU have to put a variable into the equation. YOU have to pick out something to assign to that value for x. The very idea of coming up with your own variable, and assigning a piece of the puzzle to it is what students forget to do most of the time.

Choose x as your variable, and let that equal TIME, as in the amout of time the second train is on the track.

Now if that is the case, then how long will the first train be on the track? Well, it will be all of the time the second train is on the track, plus the two hour head start. So let’s set the first train’s formula for distance equal to the second train’s formula for distance.

rate times time = rate times time

20 * (x+2) = 30 * x

20x + 40 = 30x

40 = 10x

x=4

So it will take the second train four hours to catch up, and that meeting point will be 120 miled down the road.

We can check this… train two will need six hours to cover 120 miles, and train two will need four hours to cover 120 miles, so it does check.

The other classic problem is this. They are starting far apart, and they travel towards one another. When do they meet?

Here, take their distances traveled and add them together, setting that equal to how far apart they were from each other to begin with. And again their distances have a formula, being rate times time. (big idea number one).

If they are 400 miles apart, then the equation will be:

20(x+2) + (30x) = 400

As they close in on one another, and then meet, their total distance covered will be how far apart they were to begin with.

put one line on top of the other creating parallel lines…leave plenty of space.

that or use the algebra your teacher is trying to teach you

the first train takes 6hr to reach 120 mi

the second train leaves 2hrs later and will take 4hr to reach 120mi at the same time the first one reaches 120 mi

make sure to represent the distance travelled by both during each hour of travel duration, to avoid confusion and to get an accurate count and position at any given time

20x – 30y = 0

then take the difference between x and y