Using units to solve problems: Road trip | Working with units | Algebra I | Khan Academy

We're told that Ricky is going on a road trip that is a hundred kilometers long. His average speed is 70 kilometers per hour. At that speed, he can drive five kilometers for every liter of fuel that he uses. Fuel costs 0.60 dollars per liter, so equivalent to 60 cents per liter, but they wrote it as 0.6 dollars per liter. What is the cost of fuel for the trip?

Pause the video and see if you can figure that out.

All right, so let's see what information they give us. They tell us that the trip is 100 kilometers long. They tell us that the average speed is 70 kilometers per hour, so 70 kilometers per hour. They tell us that at that speed, he can drive five kilometers for every liter of fuel that he uses, so five kilometers per liter.

Then they tell us that fuel costs 0.60 dollars per liter. So then, this last piece of information right over here is that fuel costs 0.60 dollars per liter. Normally, we would see that written as 60 cents per liter, but let's just go with it this way.

So, it's going to be useful for the total cost of the fuel for the trip. Well, we need to figure out how much fuel we're going to use and then multiply that times the cost of the fuel. So how much fuel are we going to be using?

Let's see, we're going a hundred kilometers; that's the total distance. This tells us essentially how many liters we're going to have to use over those 100 kilometers. Now, you might say: how exactly does that work? Well, if I'm going 5 kilometers per liter, if I were to take the reciprocal of this information, I would get one-fifth of a liter per kilometer. That's how much fuel I use per kilometer: one-fifth of a liter.

So why is that useful? Well, if I take 100 kilometers and if I were to multiply it times one-fifth of a liter per kilometer, this is going to tell you that over the course of this trip, I am going to use 100 times one-fifth liters. This tells us that over the course of the trip, we are going to use 20 liters.

Then, if we were to multiply that times the cost of fuel per liter, well, then we know how much the cost of our trip is. So let's do that then. Let's multiply this times 0.60 dollars per liter, which is the same thing as multiplying this times 0.60 dollars per liter. The liters cancel out, so it's good that our units work out; we're left with just dollars here.

So, 20 times 0.60 is going to get us 12. So we are left with 12. And we're done! That's the cost of our trip.

And I know what you're thinking: wait, we didn't use the information right over here that he's traveling an average speed of 70 kilometers per hour. It's true we did not use it in our calculation; although, it was kind of useful because we had to know what his fuel efficiency is at that speed.

So they're saying they're traveling at 70 kilometers per hour, and then at that speed, we get this fuel efficiency. Now, they could have just told us; they didn't even have to tell us this. They could have just told us at whatever speed he's going his fuel efficiency is this, and we still would have been able to figure out the total cost of the fuel for the trip.