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Rates & proportional relationships: gas mileage

Sal chooses equations that give a faster rate than the relationship given in a table. Created by Sal Khan.

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  • mr pants pink style avatar for user candee sutton
    I get confused sometimes. Is the coefficient x, Or is the number 65 the coefficient? I find it difficult to tell which one is which sometimes, I just don't really understand or think that it makes very much sense.
    (12 votes)
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  • starky sapling style avatar for user Navarrette, Steyvi
    i still do not understand it how did he get 60mph from 4 hours and 240 miles.
    (6 votes)
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    • duskpin ultimate style avatar for user Polina Vitić
      Think about how mph means "miles per hour" - you can write it in fraction form like this:

      miles
      -------
      hour

      Now, let's take the given information (4 hours & 240 miles) and plug the numbers into this fraction:

      240 miles
      ------------- = 240 / 4 miles per hour = 60 mph
      4 hours

      Hope this helps!
      (24 votes)
  • piceratops tree style avatar for user kcmonkeyboy07
    i must be brain dead cuz i am having a hard time figuring this out
    (12 votes)
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  • blobby green style avatar for user Lopez Caleb
    Is the coefficient x or y
    (8 votes)
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  • starky seed style avatar for user STOVALLTA
    can you show me more about graphs
    (4 votes)
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  • blobby green style avatar for user Dezirae Lord
    Hi! I understand what you're doing with the whole numbers but I'm working with decimals and don't understand what to do. Please help. Here is the problem I'm working with.
    Company A. Company B
    C=15+0.10n. C=0.25n
    For what number of brochures are the costs the same for both companies? What method should I use?
    (1 vote)
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  • blobby green style avatar for user isabella.shaffer
    Maria and Nadia drive from Philadelphia to Toronto to visit their friend. They take two days for the trip, stopping along the way for sightseeing. To conserve on gas mileage, they drive at a constant speed for the entire trip. All right, which of the following equations, where x represents hours, and y represents miles, represents a speed that is greater than Maria and Nadia's speed? Select all that apply. So let's think about what's happening here. So on day one, they travel for 4 hours and they go 240 miles. So if we wanted to figure out their speed, you would figure out distance divided by time. So they travel 240 miles in 4 hours. 240 miles divided by 4 hours is 60 miles per hour. So they were going 60 miles per hour. And assuming they went on a constant speed the whole time, they should have been going 60 miles per hour on day two as well. And we can verify that. 60 miles per hour times 5 hours is indeed 300 miles, or 300 divided by 5 is 60. So they went 60 miles per hour. So which of these equations represent a relation between time elapsed in hours and distance that represents faster than 60 miles per hour. Well, here, you're taking the time times 60 to get distance, which is what we did over here. Time times 60 to get distance, which is exactly their speed. But we care about a speed that is greater. And so pretty much all of these other coefficients are faster. So here you're taking your time times 65 miles per hour to get-- So you're going to go more distance, more than 60 miles per hour, in this situation. Here, you're going 70 miles per hour. Here you're going 80 miles per hour. And we got it right. Let's do one more. Some vinyl records, let's call them oldies, rotate at the rate of 78 revolutions per minute. The chart below shows revolutions per minute for three different tracks on another type of vinyl record called goodies. Which has a greater rate of revolution, oldies or goodies? So oldies are at 78 revolutions per minute. Let's think about these revolutions per minute right over here. So in three minutes, this one makes 135 revolutions. So how many per minute? So if we divide revolutions by minutes, you're going to get, let's see, 3 goes into 135-- it looks like it would go into, let's see, 3 goes into 120 40 times. So it looks like it goes 45 times. So it's 45 revolutions per minute for track one. Track two is also 45. 4 times 45, if I have 45 revolutions per minute times 4 minutes, that's 160 plus 20. Yep, that's 180. So these are all 45 revolutions per minute you can multiply 5 minutes times 45 revolutions per minute. You're going to get 225. So the oldies go at 78 RPM. So they do 78 revolutions in a minute, while the goodies go 45. So the oldies do more revolutions in a minute. So oldies have a greater rate of revolutions per minute, or they just have a greater rate of revolutions per minute. Right?
    (5 votes)
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  • leafers ultimate style avatar for user Hana
    What does revolution mean?
    Please make it easy for me to understand^^;
    thanks!
    (4 votes)
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  • blobby green style avatar for user asta3238
    How do you find the constant rate of change?
    (2 votes)
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  • blobby green style avatar for user imora0018
    i still do not understand it how did he get 60mph from 4 hours and 240 miles.
    (3 votes)
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    • hopper cool style avatar for user Philip
      He divided 240 by 4 to find the average. Since mph is "miles per hour" dividing the 4 hours by 4 let's us find the value equivalent to 1 hour, and to find the average we divide the 240 by 4 as well, which equals 60(mph).
      (1 vote)

Video transcript

Maria and Nadia drive from Philadelphia to Toronto to visit their friend. They take two days for the trip, stopping along the way for sightseeing. To conserve on gas mileage, they drive at a constant speed for the entire trip. All right, which of the following equations, where x represents hours, and y represents miles, represents a speed that is greater than Maria and Nadia's speed? Select all that apply. So let's think about what's happening here. So on day one, they travel for 4 hours and they go 240 miles. So if we wanted to figure out their speed, you would figure out distance divided by time. So they travel 240 miles in 4 hours. 240 miles divided by 4 hours is 60 miles per hour. So they were going 60 miles per hour. And assuming they went on a constant speed the whole time, they should have been going 60 miles per hour on day two as well. And we can verify that. 60 miles per hour times 5 hours is indeed 300 miles, or 300 divided by 5 is 60. So they went 60 miles per hour. So which of these equations represent a relation between time elapsed in hours and distance that represents faster than 60 miles per hour. Well, here, you're taking the time times 60 to get distance, which is what we did over here. Time times 60 to get distance, which is exactly their speed. But we care about a speed that is greater. And so pretty much all of these other coefficients are faster. So here you're taking your time times 65 miles per hour to get-- So you're going to go more distance, more than 60 miles per hour, in this situation. Here, you're going 70 miles per hour. Here you're going 80 miles per hour. And we got it right. Let's do one more. Some vinyl records, let's call them oldies, rotate at the rate of 78 revolutions per minute. The chart below shows revolutions per minute for three different tracks on another type of vinyl record called goodies. Which has a greater rate of revolution, oldies or goodies? So oldies are at 78 revolutions per minute. Let's think about these revolutions per minute right over here. So in three minutes, this one makes 135 revolutions. So how many per minute? So if we divide revolutions by minutes, you're going to get, let's see, 3 goes into 135-- it looks like it would go into, let's see, 3 goes into 120 40 times. So it looks like it goes 45 times. So it's 45 revolutions per minute for track one. Track two is also 45. 4 times 45, if I have 45 revolutions per minute times 4 minutes, that's 160 plus 20. Yep, that's 180. So these are all 45 revolutions per minute you can multiply 5 minutes times 45 revolutions per minute. You're going to get 225. So the oldies go at 78 RPM. So they do 78 revolutions in a minute, while the goodies go 45. So the oldies do more revolutions in a minute. So oldies have a greater rate of revolutions per minute, or they just have a greater rate of revolutions per minute.