Systems and rate problems 3

Algebra

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Systems and rate problems 3 Systems and rate problems 3

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Systems and rate problems 3

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A jogger and a walker set out at 9:00 AM from the same
point, headed in the same direction.
The average speed of the jogger is 1 mile per hour
slower than twice the speed of the walker.
So that's going to be an equation right there.
The average speed of the jogger is 1 mile per hour
slower than twice the speed of the walker.
And then they say, in 2 hours, the jogger is 3 miles ahead of
the walker.
That's going to be another equation.
In 2 hours, the jogger is 3 miles ahead of the walker.
Find the rate of the jogger.
So let's write down that first statement in equation form.
The average speed of the jogger, let's call that the
speed of the jogger.
That's the average speed of the jogger is 1 mile per hour
slower than twice the speed of the walker.
So that's equal to 2 times the speed of the
walker, minus 1, right?
It's 1 mile per hour slower than twice the
speed of the walker.
So that's that first statement.
And then they say, in 2 hours, the jogger is 3 miles ahead of
the walker.
So if we go 2 hours into the future.
So in 2 hours, the second statement is the jogger is 3
miles ahead of the walker.
So we could say that the distance that the jogger has
traveled, so the distance of the jogger, is 3 miles more
than the distance of the walker.
It is equal to the distance of the walker plus 3.
That's all I'm saying.
This is how far the jogger's traveled.
He's traveled 3 miles more than the walker.
Now right now I have two equations with four unknowns.
That's not cool.
But they've given us some information.
They said this has happened after 2 hours.
So we can express the distances they've traveled in
terms of the speed they traveled at.
Just as a bit of a review, distance is equal to rate
times time.
In this situation, the time is 2.
The rate is the speed of each person.
So we can figure out the distance.
So if you want to know the distance that the jogger
traveled, that's just going to be 2 hours times the speed of
the jogger.
So it's just going to be 2 times the speed
of the jogger, right?
Distance is equal to rate times time,
or time times rate.
Either way.
What's the distance of the walker?
Well, it's going to be 2 hours times the speed
of the walker, right?
Distance is equal to rate times time.
So now we can rewrite this equation in terms of the
speeds of the jogger and the walker.
So this equation right here.
We can rewrite it as, instead of writing the distance of the
jogger, we could write 2 times the speed of the jogger--
that's that right there-- is equal to-- instead of writing
the distance of the walker, we could write 2 times the speed
of the walker, make sure that's a subscript-- speed of
the walker plus 3.
Now we have two equations and two unknowns, and it looks
pretty tempting to eliminate one of the variables.
In particular, we have a 2 times the speed of the walker,
we have a 2 times the speed of the walker here.
What we can do is we can multiply this second equation
by negative 1 and then add the 2's.
Then these guys will cancel out.
So let's do that.
Actually let's do it even a better way.
Let's multiply the top equation by negative 1 and
then add them.
So let's multiply the top equation by negative 1.
This becomes a negative times the speed of the jogger.
This becomes a negative 2 times the speed of the walker.
Negative 1 times negative 1 times negative 1 is plus 1.
And now if we add these two equations.
These two guys are going to cancel out.
And what do we get?
We get 2 times the speed of the jogger minus the speed of
the jogger.
Well that's just going to be the speed
of the jogger, right?
2 of something minus 1 of something is
just 1 of that thing.
These two guys cancel out.
That was the whole point behind multiplying the top
equation by negative 1.
Then you have 1 plus 3, so the speed of the jogger is 4.
And we're done.
That's all they want us to find.
Find the rate of the jogger.
And we just figured it out.
If we also wanted to figure out the rate of the walker, we
could substitute back into this top equation right here,
or the original version of it, which was the speed of the
jogger is equal to 2 times the speed of the walker minus 1.
We know the speed of the jogger is 4, so you get 4 is
equal to 2 times the speed of the walker minus 1.
Add 1 to both sides, you get 5 is equal to 2 times the speed
of the walker.
Divide both sides by 2, and you get the speed of the
walker is 2-1/2 miles per hour.
But we didn't even have to do that.
This was the answer that the problem was looking for.

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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...

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At 2:33, Sal says "double bonds" but should say "single bonds."

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