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## Get ready for AP® Calculus

### Course: Get ready for AP® Calculus>Unit 4

Lesson 1: Word problems with multiple units

# Using units to solve problems: Road trip

In word problems that involve multiple quantities, we can use the units of the quantities to guide our solution. In this video, we find the cost of fuel for a road trip, using information that involves many different quantities, not all of which are useful for our problem. Created by Sal Khan.

## Video transcript

- [Instructor] We're told that Ricky is going on a road trip that is 100 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 .60 dollars per liter. So the equivalent of 60 cents per liter, but they wrote it as .60 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 gave 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. And 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 what'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 100 kilometers, that's the total distance. And then 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 five kilometers per liter, if I were to take the reciprocal of this information, I would get one fifth of a liter, of a liter, per kilometer. That's how much fuel I use per kilometer. One fifth of a liter. And so why is that useful? Well if I take 100 kilometers, and if I were to multiply, times 1/5th 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 1/5th liters. Or this is going to tell us that over the course of the trip, we're are going to use 20 liters. And 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 to 12. So we are left with 12 dollars. 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, 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.