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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.

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  • piceratops ultimate style avatar for user James Blagg✝
    How much would it change if it cost o.75 dollars per liter?
    (2 votes)
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    • starky tree style avatar for user Austin
      You would still use 20 liters of gas, (shown in ), because the distance and speed do not change. However; you'd be spending more per liter, and therefore the price would increase from 12 dollars to 15 dollars for 20 liters of gas.
      (3 votes)
  • blobby green style avatar for user John Murphy
    On one of the review questions similar to the road trip video I calculate that the person did not have enough fuel for the entire trip and so used all of her liters in the tank, so could not complete the trip. Your hints show the answer based on the full trip and there is no mention of refueling. Should I assume that she stopped and refueled? If so the amount given is correct, but if she only had the 20 liters of fuel she fell short of her goal, and I based my incorrect answer on that. But I probably overlooked something, which I have done several times before. Thanks for the videos and tests. You guys are great.
    (2 votes)
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  • piceratops ultimate style avatar for user πceratops
    What if there is wind or other forces helping the 🚙 move forward
    (2 votes)
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  • purple pi purple style avatar for user louisaandgreta
    How are there 1000 cubic cm per liter? Yes centiMETERS. How?
    Shouldn’t it be
    1L = 100cL
    (1 vote)
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    • mr pink green style avatar for user David Severin
      A liter is a measure of volume, but think of the volume of a cube, V=l*w*h, so cubic length units create a volume. A liter was originally defined as a kg of water under certain conditions, but then redefined as 1 liter = 1000 cm^3. So this is by definition, and your second statement is also true.
      (2 votes)
  • leafers seed style avatar for user recoco
    so when you write a rate as a fraction, does the time always go on the bottom?
    (1 vote)
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  • blobby green style avatar for user Ian
    How do you know if you should use 5L/1km or 1L/5km? Is it just a matter of cancelling the units you don't want in your answer?
    (1 vote)
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  • blobby green style avatar for user marczenwork
    At , Sal said (5 km per liter) is (1/5 liter per km) and he mentioned "reciprocal".

    Why is (5 km per liter) === (1/5 liter per km) ?
    (1 vote)
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    • cacteye blue style avatar for user Jerry Nilsson
      The definition of reciprocal is that
      if 𝑎⋅𝑏 = 1, then 𝑎 and 𝑏 are each other's reciprocal.

      With 𝑝, 𝑞 ≠ 0 we have
      (𝑝 ∕ 𝑞)⋅(𝑞 ∕ 𝑝) = 𝑝𝑞 ∕ (𝑝𝑞) = 1
      which shows that 𝑞 ∕ 𝑝 is the reciprocal of 𝑝 ∕ 𝑞.

      Let 𝑝 = 5 kilometers and 𝑞 = 1 liter

      We can then write 5 kilometers per liter = 𝑝 ∕ 𝑞

      Thereby, the reciprocal of 5 kilometers per liter is
      𝑞 ∕ 𝑝 = 1 liter ∕ (5 kilometers) = 1/5 liter per kilometer.
      (2 votes)
  • leaf grey style avatar for user ellisarchetti
    So you just multiply it all together?
    (1 vote)
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  • blobby green style avatar for user judekilos
    you could do it by hours thanks
    (1 vote)
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  • blobby green style avatar for user norinetart
    At 7 A.M. a plane leaves Boston, Massachusetts, for Seattle, Washington, a distance of 3000 mi. One hour later a plane leaves Seattle for Boston. Both planes are traveling at a speed of 300 mph. How many hours after the plane leaves Seattle will the planes pass each other?
    (0 votes)
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    • mr pink green style avatar for user David Severin
      So you have to first assume there is no wind. At 300 mph, it will take 10 hours to make the trip. So if they started at the same time, they would meet in the middle 5 hours and 1500 miles from each way. Since one starts an hour later, at 5 hours, one will be at 1500 (5*300) from Boston and the other will be 1200 (4*300) from Seattle. They are 300 miles apart, so they will meet at 150 miles which would be an extra 1/2 hour. The first would be 5 1/2 hours from Boston and the second 4 1/2 hours from Seattle.
      (2 votes)

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.