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>> This is your math gal,
Julie Harland.
Please visit my web site
at yourmathgal.com where all
of my videos are organized
by topic.
In this video we're going
to find the average rate
of a trip that has more
than one part.
So we're going
to be using the formula rate
times time equals distance.
But from this formula,
remember that if you wanted
to find the rate
or the time you could divide
the left-hand side either by R
or T. So if you divided the
both sides by T,
you would have the rate is
distance over the time.
And if you were looking
for the time you can say
that's the distance
over the rate.
All right.
So that comes
from the same formula there.
So here's our problem.
The Tron [phonetic] travels 30
miles to work doing an average
rate of 45 miles per hour,
it travels the 30 miles home
at a rate of 60 miles
per hour.
What is the average rate
for the entire time driving to
and from work?
Well, first of all a lot
of people think
that you can just take these
miles per hour
and take the average.
In other words, they say,
well, it's 30 miles there,
30 miles home.
So if you go 40 miles per hour
and 60 miles per hour home,
isn't the average rate 50
miles per hour?
And as it turns out,
it's close
to 50 miles per hour
but it's not exactly that.
If you're taking a multiple
choice test,
you'll see that as one
of the possibilities.
They'll just put 50 miles per
hour, but that will be wrong.
So let's figure
out how you would do this
problem correctly.
So what we want
to do is figure
out the total time of the trip
because if we know the total
distance and the total time
we'll be able to figure
out the rate.
Now the total distance, well,
it's 30 miles there
and 30 miles back.
So hopefully
that makes sense to you.
You're going
to have 60 miles
total distance.
But we don't--
let's figure
out the time it takes
to drive to work.
So we're trying to figure
out the time.
So we're going to use
that formula,
it's just distance over rate.
So the time is just going
to be, in this case,
distance over rate--
30 over 40.
Now, it's going to be in hours
because notice the rate's
in miles per hour.
All right.
So if the rate's
in miles per hour,
we want the distance to be
in miles and the time
to be in hours.
So this is three-fourths
of an hour or--
write it like that,
three-fourths of an hour
if you reduce it.
All right.
What about going home?
Same formula, right?
Distance over rate.
So the time it takes
to get home is 30-60ths
of an hour or half an hour.
>> Now the first thing you
should do is see
if these numbers I'm coming
up with make common sense
to you.
So it's 30 miles to work.
You're only going 40 miles per
hour so you're going less
than 40 miles, so it's going
to take less than an hour
to get to work.
All right.
How about going home?
You're going 60 miles an hour.
And if you're only going 30
miles, that's only half
an hour.
That makes sense
because you should be able
to go a whole 60 miles
in one hour
and you're going half
that distance.
So hopefully this also
makes sense.
So here we go.
We've got the total distance
as 60 miles.
What about the total time?
Well, we have
to add the two times,
the time going
to work plus the time going
back home.
So that's what we do.
We're going to add those up,
three-fourths plus one half.
All right.
Now you have to remember how
to add fractions.
One way is you just get a
common denominator here
by noting that common
denominator's is 4.
So then we have the
numerator's added together,
3 plus 2 is five-fourths.
So our total time is
five-fourths, which happens
to be an hour and 15 minutes.
But basically,
it's five-fourths of an hour.
So if you know the distance
and you noted the time,
how do you get the rate?
That's what we're looking for,
right.
That's the question.
So what's the average rate?
Well, we know
that the rate is the distance
over the time.
And I'm going to write
that as D divided
by T. That's the same thing.
When you write D over T,
that's the same thing saying D
divided by T.
And since I'm working
with fractions,
I think it's easier
to write it as D divided by T.
So let's do that.
So the average rate will
be what?
Well, look up here.
Here is the distance
and here is the time.
So we've got 60 divided
by five-fourths.
All right.
How do you divide
with fractions?
So that's the same thing as 60
over 1 times the reciprocal,
four-fifths.
All right.
So we can cancel here.
And that gives me 48.
And then we're talking
about a rate.
We really want the answer
of 48 miles per hour.
Okay, so the entire trip is
saying the average trip is 48
miles per hour.
Now remember,
here's the original
problem here.
Like I said,
a lot of people will say it's
50 miles per hour.
Notice it's not 50 miles per
hour, but it's close.
It's a little less than that.
It's 48 miles per hour.
So now let's check it.
So here's the problem.
We've got 48 miles per hour.
So does it make sense
if the rate is 48 miles per
hour, and the time we said was
five-fourths,
we added the three-fourths
plus one-half,
and the distance we know is
the total of 60.
Is it true
that rate times time
equals distance?
So we're just going
to check that out.
We're going
to do rate times time,
which is 48
times five-fourths.
And let's see,
if we cancel it gives you 12.
and that gives you 12 times 5
is 60.
And does that match?
Yes, it does.
So yup, it makes sense
if we check our answer.
So this is just a little check
to make sure the rate times
the time for the total trip
makes sense, right,
because this is for--
should have maybe
written this.
This is checking our
answer here.
So this is just checking
answer for total trip.
This is your math gal,
Julie Harland.
Please visit my web site
at yourmathgal.com where all
of my videos are organized
by topic.