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>> Here's another uniform motion problem, so if you remember rate times time equals distance...
more we'll be using.
Andy and Beth are at opposite ends of an 18 mile country road, so they're apart from each other
and they are going to leave at the same time running toward each other.
So here's the picture.
They're running toward each other, and they're 18 miles apart so this total distance
that they started was 18 miles apart.
Here's the picture.
We need to make up a little chart.
We'll decide what's going to be the variable.
We're going to use A and B for Andy and Beth.
Do I know their rates?
Yes. Andy's going 7 miles an hour and Beth's going 5 miles an hour....
want to know their times.
No. Do I know anything about their time, like do they meet at the same time,
do they both go at the same amount of time, etc.?
Well they left at the same time, and then they ran toward each other.
So they each...
if Andy went X so did Beth, they went the same amount of time.
So pretty simple this time, same time, you just give the same variable.
Rate times time equals distance, so Andy's distance is 7 times X or 7X, and Beth's is 5X.
So we've got Andy 7X, Beth 5X.
Now we look at the picture.
This piece and this piece, have to add up to 18.
That's our equation.
7X plus 5X equals 18.
So 12X is 18...
divided by 12.
That gives you 1 and a half or 1.5.
So what does that mean?
That means that each ran for an hour and a half.
So let's check it.
See if it all makes sense.
Andy, Beth...
the rates we already knew, now we know their time.
I'm just going to go ahead and put 1.5 and 1.5
to get the distance you multiply 7 times 1.5.
So that's 10.5 and 5 times 1.5 is 7.5.
So Andy ran 10.5 miles and Beth ran 7.5 miles.
We can go back up here.
This is 10.5 miles, 7.5 miles.
Well does that mean they ran a total of 18 miles?
Certainly, because 10.5 plus 7.5 is 18 miles.
Now let's go to the question.
Does it ask for how many miles they ran?
No. It says, how long after they begin will they meet?
So what it's talking about is their time.
That's the answer.
They meet after 1.5 hours.
Now let's say this problem had said, they left at 4:30.
What time did they meet?
Well 1 and a half hours after 4:30 is 6 p.m. So some of them might ask you that,
where you don't do anything with the time till the end of the problem.
So you do have to make sure you go back to the question, and answer...
according to what is asked.
So they meet after 1 and a half hours.
That's all it is.
How long after they begin will they meet?