Graphing proportional relationships
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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.