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# Rates & proportional relationships: gas mileage

Videotranscript

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.