[SOUND] Let's look at distance, rate, and time.

[SOUND] For example, two trains leave the station at the same time,

one is heading west, and the other east. The westbound train travels westbound 12

miles per hour faster than the eastbound train.

If the two trains are 400 miles apart after two hours, what is the rate of the

westbound train? So, let's let x equal the rate in miles per hour of the

westbound train. Now, we're told that the westbound train

travels 12 miles per hour faster than the eastbound train.

Which means, the eastbound train travels two miles per hour slower than the

westbound train. Therefore, if x is equal to the rate of

the westbound train, then x-12 is equal to the rate in miles per hour of the

eastbound train. Now, we're going to use the famous

formula, the distance is equal to rate times time to help us solve this problem.

Or in symbols, d = r * t. Now, let's keep track of things in a

table here. So, here's r for rate, here's t for time,

and here's d for distance. And here is the westbound train, and here

is the eastbound train. So, x is the rate of the westbound train,

x-12 is the rate of the eastbound train. And we know something, about how far

apart the trains are, after two hours. So, we're going to let t = 2 here.

Which means, after two hours, the distance that the westbound train has

traveled, is r * t or 2x. And the distance after two hours that the

eastbound train has traveled is 2 * x-12. So, if here's the station,

and after two hours the distance that the eastbound train has traveled is 2 * x-12,

and the distance that the westbound train has traveled after two hours is 2 * x.

But we're told that after those two hours, these two trains are 400 miles

apart. Which means, this total distance is 400.

That is the sum of those two distances has to be 400.

Namely, 2x + 2 * x-12 = 400, or 2x + 2x - 24.

= 400, or 4x - 24 = 400. And then, adding 24 to both sides, we get

4x = 424. And then, dividing both sides by 4 gives

us the x, which is the rate we're looking for at the westbound train, is 106 miles

per hour. And this is an example of how we use this

very important formula here, distance is equal to rate times time.

Thank you, and we'll see you next time. [SOUND]