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We are on problem 17.
Alice and Corinne stand back-to-back.
They each take 10 steps in opposite directions away from
each other and stop.
Alison turns around walks towards Corinne and reaches
her in 17 steps.
OK, so this is interesting.
So they're back-to-back.
Let's say Alice goes this way.
And let's say A is for Alice steps.
So 10 Alice steps, we don't know how long Alice steps are.
And then Corinne had gone this way and taken 10 Corinne
steps, right?
C is, I don't know how long she takes per step, two feet?
Who knows?
But C is the distance of Corinne steps in my little
world right here.
OK, so they took ten steps in opposite directions from each
other and stopped.
Alison turns around and walks towards Corinne and reaches
her in 17 steps.
So this is where Corinne is now, right?
So this whole distance here is 17 Alice steps.
The length of one of Alice steps is how many times the
length of one of Corinne's steps?
And they say, all of Alice's steps are the same length, and
all of Corinne's steps are the same length.
Well we know a couple of things.
We know to get to here would have been 10
Alice steps, right?
This would have been 10 Alice steps.
So essentially, in the same distance that Corinne took 10
steps, Alice took what?
She took 7 steps, right?
She took 10 to get to the middle, and then 7 more to get
to where Corinne is.
So this is 7 Alice steps.
So 7 times Alice step length is equal to 10 times Corinne
step length, right?
I'm just saying 7a is equal to 10c.
And what do we want to know?
We want to know the length of one of Alice's steps is how
many times the length of one of Corinne's steps?
So we want to solve for a.
So Alice's step is equal to-- divide both sides by 7-- is
equal to 10/7 times a Corinne step.
And that's our answer, 10/7.
Next problem, problem 18.
Let the function f be defined by f of x is equal to x
squared plus 18.
If m is a positive number such that f of 2m is equal to 2 f
of m, what is the value of m?
A lot of people get intimidated by these function
problems, but in some ways they're kind of the most
straightforward problems. You just have to sit
and evaluate them.
So what's f of 2m?
So everywhere we see an x, we put a 2m.
So it's 2m squared plus 18, right?
Wherever I saw an x, I put a 2m.
And that equals 2 times f of m.
So wherever I see an x, I put an m.
So that's m squared plus 18.
Now I just simplify.
2m squared, that's equal to 4m squared plus 18 is equal to 2m
squared plus 36.
I just distributed the 2.
So you subtract 2m squared from both sides, you get 2m
squared plus 18 is equal to 36.
I subtracted this from both sides.
Subtract 18 from both sides, you get 2m
squared is equal to 18.
Divide both sides by 2, you get m squared is equal to 9.
And then you get m is equal to-- if you just did this
straight off, you'd get plus or minus 3.
But they tell us that m is a positive number, so we know
that m is equal to 3.
And we are done.
And that's it.
I'll see you in the next section.