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### Course: Geometry (all content) > Unit 17

Lesson 1: Worked examples- Challenge problems: perimeter & area
- Challenging perimeter problem
- CA Geometry: Deductive reasoning
- CA Geometry: Proof by contradiction
- CA Geometry: More proofs
- CA Geometry: Similar triangles 1
- CA Geometry: More on congruent and similar triangles
- CA Geometry: Triangles and parallelograms
- CA Geometry: Area, pythagorean theorem
- CA Geometry: Area, circumference, volume
- CA Geometry: Pythagorean theorem, area
- CA Geometry: Exterior angles
- CA Geometry: Pythagorean theorem, compass constructions
- CA Geometry: Compass construction
- CA Geometry: Basic trigonometry
- CA Geometry: More trig
- CA Geometry: Circle area chords tangent
- Speed translation

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# Speed translation

Sal converts feet to inches to help solve a rate problem. Created by Sal Khan.

## Want to join the conversation?

- How to tell when two different people do the same task at different speeds, how long would it take them to do the task once together.

For example: It takes Sam 12 minutes to sweep a sidewalk. It takes Billy 15 minutes to sweep the same sidewalk. How long would it take for them, working together, to sweep the sidewalk?(8 votes)- You first need to find the rates (actions per time, instead of time per action), which can be done by inverting: Sam sweeps the sidewalk in 12 minutes, which means that he can do 1/12 of the sidewalk per minute. Billy sweeps the sidewalk in 15 minutes, which is 1/15 of the sidewalk per minute. Together, their speed is 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20 of the sidewalk per minute. Since this is a rate (sidewalk per minute) you can invert it to get minutes per sidewalk. 20/3 = 6 2/3 minutes for them to do the sidewalk together.(16 votes)

- I cannot understand why Sal divides 336 inches per minutes to 60, instead of multiplying by 60. The number for inches per seconds shouldn't be greater than 5,6?(2 votes)
- One hour is 60 minutes, right? So if we wanted to convert 60 minutes to 1 hour, then when would divide by 60. Same here. So if we have 336 in/min, then we have to divide by 60 to transform minutes to hours. Hope that helps!(0 votes)

- I want to be good at math like this so bad!(2 votes)
- That is the kind of attitude that will get you somewhere in life! Keep it up!(2 votes)

- what do you divide by?(2 votes)
- how can you tell what speed you are going(1 vote)
- This is more of a general question than just a question related to this specific problem. It's hard to answer it.

It's because there are many ways to know how fast you're going, say in a car, or running, or whatever. I think it might be better to research into speed to learn the full answer ^^(2 votes)

- how much is a gram?(1 vote)
- The propeller aircraft made the trip in 9 hours. The jet aircraft made the trip in 4 hours. Find the rates of each if the jet aircraft flew 500 miles faster than the propeller aircraft(1 vote)
- Let X = rate of propeller aircraft

Let X+500= rate of jet aircraft

This problem assumes you know the formula: Distance = Rate * Time.

Distance of propeller aircraft = 9x

Distance of jet aircraft = 4(x+500)

Since the 2 plans fly the same distance (the same trip), we can set these equal to each other.

9x = 4(x+500)

Solve for X (the speed of the propeller plane)

Once you have X, you can find X+500 (the speed of the jet plane).

Hope this helps.(2 votes)

- Units are another way of saying number, if your talking about unit RATES then thats a different thing. A unit is a number.(1 vote)

- some of the questions are answerable but some are not. why is this? is there a way to answer it?(1 vote)
- Oh, Im sorry but Im Australian, and I don't understand how much 1 Inch is and how much 1 Mile is because we use Centimetres and Kilometres.

So can anybody tell me how much 1 Inch is and how much 1 Mile is.

That would be great.Thanks.(1 vote)- Thanks ftsk8ter now i can actually watch this video better(1 vote)

## Video transcript

Welcome to the
presentation on units. Let's get started. So if I were to tell you -- let
me make sure my pen is set up right -- if I were to tell you
that someone is, let's say they're driving at a speed
of -- let's say it's Zack. So let's say I have Zack. And they're driving at a
speed of, let me say, 28 feet per minute. So what I'm going to ask you is
if he's going 28 feet in every minute, how many inches will
Zack travel in 1 second? So how many inches per second
is he going to be going? Let's try to figure
this one out. So let's say if I had 28, and
I'll write ft short for feet, feet per minute, and I'll
write min short for a minute. So 28 feet per minute, let's
first figure out how many inches per minute that is. Well, we know that there are
12 inches per foot, right? If you didn't know
that you do now. So we know that there
are 12 inches per foot. So if you're going 28 feet per
minute, he's going to be going 12 times that many
inches per minute. So, 12 times 28 -- let me do
the little work down here -- 28 times 12 is 16, 56 into 280. I probably shouldn't be
doing it this messy. And this kind of stuff it would
be OK to use a calculator, although it's always good to
do the math yourself, it's good practice. So that's 6, 5 plus 8 is 13. 336. So that equals 336
inches per minute. And something interesting
happened here is that you noticed that I had a foot in
the numerator here, and I had a foot in the denominator here. So you can actually treat
units just the same way that you would treat actual
numbers or variables. You have the same number in the
numerator and you have the same number in the denominator, and
your multiplying not adding, you can cancel them out. So the feet and the feet
canceled out and that's why we were left with
inches per minute. I could have also written
this as 336 foot per minute times inches per foot. Because the foot per minute
came from here, and the inches per foot came from here. Then I'll just cancel this
out and I would have gotten inches per minute. So anyway, I don't want
to confuse you too much with all of that unit
cancellation stuff. The bottom line is you just
remember, well if I'm going 28 feet per minute, I'm going to
go 12 times that many inches per minute, right, because
there are 12 inches per foot. So I'm going 336
inches per minute. So now I have the question, but
we're not done, because the question is how many inches am
I going to be traveling in 1 second. So let me erase some of the
stuff here at the bottom. So 336 inches -- let's write it
like that -- inches per minute, and I want to know how
many inches per second. Well what do we know? We know that 1 minute -- and
notice, I write it in the numerator here because I want
to cancel it out with this minute here. 1 minute is equal to
how many seconds? It equals 60 seconds. And this part can be confusing,
but it's always good to just take a step back and think
about what I'm doing. If I'm going to be going 336
inches per minute, how many inches am I going to
travel in 1 second? Am I going to travel more
than 336 or am I going to travel less than
336 inches per second. Well obviously less,
because a second is a much shorter period of time. So if I'm in a much shorter
period of time, I'm going to be traveling a much
shorter distance, if I'm going the same speed. So I should be dividing by a
number, which makes sense. I'm going to be dividing by 60. I know this can be very
confusing at the beginning, but that's why I always want you to
think about should I be getting a larger number or should I be
getting a smaller number and that will always give you
a good reality check. And if you just want to look at
how it turns out in terms of units, we know from the problem
that we want this minutes to cancel out with something
and get into seconds. So if we have minutes in the
denominator in the units here, we want the minutes in the
numerator here, and the seconds in the denominator here. And 1 minute is equal
to 60 seconds. So here, once again,
the minutes and the minutes cancel out. And we get 336 over 60
inches per second. Now if I were to actually
divide this out, actually we could just divide the numerator
and the denominator by 6. 6 goes into 336,
what, 56 times? 56 over 10, and then we can
divide that again by 2. So then that gets us 28 over 5. And 28 over 5 -- let's see, 5
goes into 28 five times, 25. 3, 5.6. So this equals 5.6. So I think we now just
solved the problem. If Zack is going 28 feet in
every minute, that's his speed, he's actually going
5.6 inches per second. Hopefully that kind
of made sense. Let's try to see if we
could do another one. If I'm going 91 feet per
second, how many miles per hour is that? Well, 91 feet per second. If we want to say how many
miles that is, should we be dividing or should
we be multiplying? We should be dividing
because it's going to be a smaller number of miles. We know that 1 mile is equal to
-- and you might want to just memorize this -- 5,280 feet. It's actually a pretty
useful number to know. And then that will actually
cancel out the feet. Then we want to go from
seconds to hours, right? So, if we go from seconds to
hours, if I can travel 91 feet per second, how many will I
travel in an hour, I'm going to be getting a larger number
because an hour's a much larger period of time than a second. And how many seconds
are there in an hour? Well, there are 3,600
seconds in an hour. 60 seconds per minute and
60 minutes per hour. So 3,600 over 1
seconds per hour. And these seconds
will cancel out. Then we're just left with, we
just multiply everything out. We get in the numerator,
91 times 3,600, right? 91 times 1 times 3,600. In the denominator
we just have 5,280. This time around I'm actually
going to use a calculator -- let me bring up the calculator
just to show you that I'm using the calculator. Let's see, so if I say 91 times
3,600, that equals a huge number divided by 5,280. Let me see if I can type it. 91 times 3,600 divided
by 5,280 -- 62.05. So that equals 62.05
miles per hour.