Chapter 6 Lesson 1
Distance and Rate Problems
Changing feet
per second into mph.
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Adjust your screen
for correct lettering.
I've been planning this for awhile.
Is it my last math lesson?
I bet you're quitting and
going to write a book about me.
I thought about that last week,
but nobody would pay me.
I think they're waiting for
the TV show to come out first,
then they'll buy the book.
No TV show, book, or movie.
This is 1 of those moments that
will change how you do math.
You said that about variables
and equations. I didn't change.
What's different this time?
Feet per Second
Now we'll think of speed as
feet per second instead of mph.
Why are you changing
miles per hour? I like that.
You're sitting in your red Corvette
at a stop light. It turns green.
Does it take hours for you to
accelerate from a light?
Are you kidding me?
Give me 3 seconds and I'm down
the road. 4 and I'm almost home.
That's why feet per second.
Miles per hour works with
long trips, but we want to study
how cars accelerate in seconds.
So, why change to feet per second?
5,280
feet in a mile
Ok, you do the math to find the
feet a car goes in 5 seconds.
So, how do you use this
feet per second thing?
We'll start out with the
easy ones, the 10s. Start out
by counting mph in 10s.
Works for me. I'm pretty
good at counting 10s.
10 feet/second
Here's an easy one.
There's only 1 ten to count.
There is a 2nd step.
Multiply x 7
Now, multiply how many
10s there are times 7.
So 10 ft/s is 1 x 7, 7 mph.
1x7=7
mph
Count 10s
Here it is. If you were biking
10 ft per sec that's 7 mph.
I'll make one up going faster.
40 feet per second
If you're going 40 ft per second,
how fast is that in miles per hour?
What's the 1st step?
40 is 4 tens
Count the 10s. 40 has 4 tens.
40 is 4 tens
What do you multiply 4 by?
4 x 7 = ? mph
Multiply 4 x 7 because
there's 4 10s in 40 mph.
Ok, I know the answer.
4 x 7 = 28 mph
So, if you ride your bike
40 feet per second, that's 28 mph.
4 x 7 = 28 mph
Down a hill with the
wind behind you, maybe.
Think about the 2 steps.
1. Count the 10s
2. Multiply by 7
Looks like 2 simple steps.
How about going faster?
90 feet per second
Change 90 ft per second to mph.
Solve it mentally, all in 1 step.
9 x 7 = 63 mph
9 tens x 7 is 63
That's how fast a car would go.
Ok, I have a question.
90 feet per second
How am I going to
remember to multiply x 7?
90 Feet per Second
See the F in feet?
Think about it like reverse 7.
90 Feet per second
That's alittle strange,
but it might work.
Oooh, here's another question.
15 feet per second
What if it's in between 10s?
Like it's 15 feet per second.
15 feet per second
How did we solve
imperfect square roots?
40 feet per second
Find the perfect roots.
Then estimate which one's closer.
15 feet/second
10
20
30
40
50
7
14
21
28
35
Here's 15 mph.
Which ones is it between?
15 feet/second
10
20
30
40
50
7
14
21
28
35
It's between 7 and 14.
15 ft/sec
is about 10 mph.
So, estimate it. It's about 10 mph.
Here, I made some steps.
1. Count the 10s
2. Multiply by 7
That's how feet
per second makes mph.
Do you really mean that's
how far they go in 1 second?
That's what feet per second is.
You can use a stopwatch
to find the seconds they went.
Like I really have a stopwatch.
Or use the time it takes to say
1 thousand. That's about a second.
I see. So, 2 seconds is about,
1 thousand, 2 thousand.
Ok, when do I use
feet and miles per hour?
MPH Feet/Second
Depends on the problem.
But, and this is a big but, it's a
lot easier measuring feet per
second, so we'll use feet/second.
Qs
Why are feet per second
important to story problems?
Hours can't measure how
fast a car accelerates.
Use feet per second instead.
Name 2 steps to change feet per
second (in 10s) to be mph.
1. Count the 10s
2. Multiply by 7
Multiply the number of 10s x 7.
60 ft per second
If a car is going 60 ft per second,
how many miles per hour is that?
6 x 7 = 42
mph
6 tens
Count the 10s and multiply x 7.
So 60 ft/s is 6 x 7, 42 mph.
Chapter 6 Lesson 1a
Distance and Rate Problems
Changing miles per hour
into feet per second.
I was telling my dad how to
change feet per second to mph.
What did he say about it?
The usual, "They didn't teach
that when I was in school."
Is that really true?
They still used it. They just
didn't know how to change them.
Then he said, "We're going 50 mph.
How fast is that in feet per second?"
I said we still have to learn it.
Good question. I guess we'll go
over it today. I'll start off simpler.
10 mph = ? Ft/sec
If you're going 10 mph, how
many feet per second is that?
First, count the 10s.
10 mph is 1 ten
10 mph would be 1 ten.
Do you multiply it?
1 x 15 = 15
ft/sec
1 ten
Multiply times 15.
That's 15 feet per second.
Here's what it looks like.
10 mph is about 15 ft/sec.
I'll make a faster one.
50 mph
Change 50 mph
to feet per second.
Again, how many 10s are in 50?
50 mph
That would be 5 tens.
Does that multiply by 15?
5 x 15 = ?
ft/sec
5 tens
Exactly, multiply times 15.
What's the answer?
5 x 15 = 75
ft/sec
5 tens
75 feet per second.
Wow, that's really simple.
Is the answer pretty close?
60 mph
We'll use 60 mph to find out.
How many 10s in 60 mph?
60 mph
That would be 6 tens.
I know how to multiply it.
6 x 15 = 90
6 tens
60 mph is about
90 feet per second.
Ok, how close it it really?
ft/sec
60 x 5280 = 316,800
There's the feet in 1 hour.
Now, divide by 3600.
60 x 5280 = 316,800
Why divide by 3600?
316,800
3600
60 times 60 finds
the seconds in 1 hour.
Let's see how close it is to 90.
316,800 3600 = 88
Wow, 88 is only 2 feet per
second off from 90.
Ok, this is my math.
This isn't in books, but I want you
to know how feet per second works.
Would you write those again?
Feet Per Second to MPH
Count the 10s and multiply x 7.
This is the one we'll use to
estimate MPH from ft per sec.
My dad wants the other one.
This is the one you use in a car
and you want feet per second.
I'm going to get my dad with this.
He's going to flip his eyeballs.
Flip his eyeballs?
Sounds interesting.
Why is that so important?
He thinks I'm not very bright.
I'll tell him how fast we're going
in feet per second. He'll like that.
Too bad your dad's like that.
That's ok. Now I know
something he doesn't know.
Qs
Name 2 steps to change mph
to feet per second.
1. Count the 10s.
2. Multiply by 15.
Multiply the number of 10s x 15.
20 mph
How do you estimate
20 mph as feet per second?
2 x 15 = 30
ft/sec
2 tens
1. Count the 10s, 2.
2. Multiply x 15 is 30.
Chapter 6 Lesson 1
Distance and Rate Problems
Short Lesson
Change feet per second
into mph and back.
Miles Per Hour
We've use miles per hour and
measured trips using hours.
We'll make a major change in
how we talk about measuring trips.
Feet Per Second
If we want to count trips in seconds
we need to use feet per second.
This lesson estimates how feet per
second change into miles per hour.
10 ft/sec = ? mph
Start out counting 10s.
There is a 2nd step.
Multiply x 7
There's 1 10, so multiply 1 x 7.
10 feet per second is
about how many mph?
1 x 7 = 7 mph
There's 1 10, so multiply 1 x 7.
10 feet per second
is about 7 mph.
We'll try a faster one.
40 feet per second
If you're going 40 ft per second,
find how fast it is in miles per hour.
What's the 1st step?
40 is 4 tens
Count the 10s.
What's the 2nd step
to find miles per hour?
4 x 7 = 28 mph
If you ride your bike 40 feet
per second, that's 28 mph.
Now we'll go backwards.
mph to feet/second
Now we'll change mph
to feet per second.
We'll make a problem.
10 mph = ? ft/sec
If you're going 10 mph, the
1st step is the same as before.
First, count the 10s in 10 mph.
10 mph = ? ft/sec
There's 1 ten in 10 mph.
Now, instead of 7, multiply by 15.
How many feet per second is it?
1 x 15 = 15
10 mph = 15 ft/sec
10 mph is about
15 feet per second.
We'll do 1 more problem.
30 mph
Find the 10s in 30 mph.
What does it multiply times?
3 x 15 = 45
30 mph = 45 ft/sec
30 mph is about
45 feet per second.
Here's what we just did.
Feet Per Second to MPH
Count 10s. Multiply x 7.
MPH to Feet Per Second
Count 10s. Multiply x 15.
Questions
Why are feet per second
important to acceleration?
Acceleration is
measured in seconds.
Use the same unit
that the problem uses.
How can you change feet per
second to estimate it's mph?
Count the 10s
Multiply x 7.
If a car is going 60 ft per second,
estimate it in miles per hour.
How many 10s are in 60 mph?
6 x 7 = 42 mph
There are 6 tens in 60.
Multiply x 7.
So 60 ft/s is 6 x 7, 42 mph.
20 mph
How can you change mph
to estimate feet per second?
Count the 10s.
Multiply x 15.
Estimate 20 mph in
feet per second.
2 x 15 = 30
# of 10s
ft/sec
1. There are 2 10s in 20.
2. Multiply by 15.
20 mph is about 30 ft/sec.
Chapter 6 Lesson 1
Distance and Rate Problems
Practice #1
Change feet per second
into mph and back.
Why are feet per second
important to story problems?
Hours can't measure how
fast a car accelerates.
Use feet per second instead.
Name 2 steps to change feet per
second (in 10s) to be mph.
1. Count the 10s
2. Multiply by 7
Multiply the number of 10s x 7.
60 ft per second
If a car is going 60 ft per second,
how many miles per hour is that?
6 x 7 = 42
mph
6 tens
Count the 10s and multiply x 7.
So 60 ft/s is 6 x 7, 42 mph.
Name 2 steps to change mph
to feet per second.
1. Count the 10s.
2. Multiply by 15.
Multiply the number of 10s x 15.
20 mph
How do you estimate
20 mph as feet per second?
2 x 15 = 30
ft/sec
2 tens
1. Count the 10s, 2.
2. Multiply x 15 is 30.
Problems
50 feet/second
A car is going 50 ft per second.
What is the 1st step to find mph?
5 10s in 50 ft/sec
Count the number of 10s.
There are 5 tens in 50.
What is the 2nd step?
5 x 7 = 35 mph
Multiply x 7.
50 ft/s is 5 x 7, 35 mph.
20 feet/second
20 ft per second. All in 1 step,
estimate the mph.
2 x 7 = 14 mph
There are 2 tens in 20.
Multiply x 7.
20 ft/s is 2 x 7, 14 mph.
30 feet/second
Estimate the mph
for 30 ft per second.
3 x 7 = 21 mph
There are 3 tens in 30.
Multiply x 7.
30 ft/s is 3 x 7, 21 mph.
200 feet/second
200 ft per second.
How many mph is it about?
20 x 7 = 140 mph
There are 20 tens in 200.
Multiply x 7.
200 ft/s is 20 x 7, 140 mph.
Chapter 6 Lesson 1
Distance and Rate Problems
Practice #2
Change feet per second
into mph and back.
Why are feet per second
important to story problems?
Hours can't measure how
fast a car accelerates.
Use feet per second instead.
Name 2 steps to change feet per
second (in 10s) to be mph.
1. Count the 10s
2. Multiply by 7
Multiply the number of 10s x 7.
60 ft per second
If a car is going 60 ft per second,
how many miles per hour is that?
6 x 7 = 42
mph
6 tens
Count the 10s and multiply x 7.
So 60 ft/s is 6 x 7, 42 mph.
Name 2 steps to change mph
to feet per second.
1. Count the 10s.
2. Multiply by 15.
Multiply the number of 10s x 15.
20 mph
How do you estimate
20 mph as feet per second?
2 x 15 = 30
ft/sec
2 tens
1. Count the 10s, 2.
2. Multiply x 15 is 30.
Problems
20 mph
A car is going 20 miles per hour.
Estimate it in feet per second.
What's the 1st step?
2 tens in 20 mph
# of 10s
1. Count the 10s.
What's the 2nd step?
2 x 15 = 30
# of 10s
ft/sec
1. Count the 10s.
2. Multiply that by 15.
20 mph is about 30 ft/sec.
60 mph
A car is going 60 mph.
What is that in feet per second?
6 x 15 = 90
# of 10s
ft/sec
1. Count the 10s.
2. Multiply that by 15.
60 mph is about 90 ft/sec.
40 mph
A car is going 40 mph.
What is that in feet per second?
4 x 15 = 60
# of 10s
ft/sec
1. Count the 10s.
2. Multiply that by 15.
40 mph is about 60 ft/sec.
100 mph
A car is going 100 mph.
Estimate it in feet per second.
10 x 15 = 150
# of 10s
ft/sec
1. Count the 10s.
2. Multiply that by 15.
100 mph is about 150 ft/sec.
Chapter 6 Lesson 1
Distance and Rate Problems
Performance #1
Change feet per second
into mph and back.
30 ft/sec
70 ft/sec
Estimate each in mph.
30 ft/sec
21 mph
70 ft/sec
49 mph
40 ft/sec
100 ft/sec
What are these in mph?
40 ft/sec
28 mph
100 ft/sec
70 mph
10 ft/sec
110 ft/sec
What are these in mph?
10 ft/sec
7 mph
110 ft/sec
77 mph
20 mph
50 mph
Estimate in feet per second.
20 mph
30 ft/sec
30 mph
45 ft/sec
40 mph
100 mph
Estimate the feet per second.
40 mph
60 ft/sec
100 mph
150 ft/sec
10 mph
30 mph
Estimate feet per second.
10 mph
15 ft/sec
30 mph
45 ft/sec
Chapter 6 Lesson 1
Distance and Rate Problems
Performance #2
Change feet per second
into mph and back.
20 ft/sec
60 ft/sec
Estimate each in mph.
20 ft/sec
14 mph
60 ft/sec
42 mph
30 ft/sec
120 ft/sec
What are these in mph?
30 ft/sec
21 mph
120 ft/sec
84 mph
40 ft/sec
90 ft/sec
What are these in mph?
40 ft/sec
36 mph
90 ft/sec
63 mph
30 mph
60 mph
Estimate in feet per second.
30 mph
45 ft/sec
60 mph
90 ft/sec
50 mph
70 mph
Estimate the feet per second.
50 mph
75 ft/sec
70 mph
105 ft/sec
20 mph
40 mph
Estimate feet per second.
20 mph
30 ft/sec
40 mph
60 ft/sec