00:01
All right, so question 36 is a rate question.
00:04
So with your rate questions, what we have in this case is speed, is our rate, is equal to distance divided by.
00:25
We have rory, he left home, and he went to the airport, and it says that he did 45 miles per hour on the way there.
00:39
To the airport.
00:44
And on the way back, he ran into traffic, and it was only able to go 30, i'm able to go 30 miles per hour on the way back.
00:59
If the total travel time, it's the total time of there, right, round trip there, and back is equal to 2 .5 hours, two hours and 30 minutes.
01:15
How far is it in the? miles from rory's house to the airport.
01:20
Now it is usually the best application to do a table that keeps track of all the numbers.
01:31
Usually you have like a rate table where you could solve for the different variables.
01:40
In this case, the only thing that we're solving for is distance.
01:45
All right, so distances are a variable.
01:47
And so we're going to have to multiply time over the other side, isolate distance.
01:52
So distance is equal to the speed times the distance or times the time.
02:08
Well, time we can do, we have 2 .5 hours, but the only thing that's a little bit of a problem here is that we have to solve for a algebraic expression because time is not to, 2 .5 hours for the whole thing, but rather we have an expression where time is going to be one variable, and then we have to isolate and solve for the return trip.
02:38
And so let's say on the way there, this is time t or x, but on the way back, we're going to have the leftover time, which is, is like a different variable.
02:51
We could say it's x or y, but it's a different variable from t and either way together they're going to add up to equal to 2 .5 which means that this is going to be equal to 2 .5 minus t um and so solving for this right we have two speeds we have a speed there right and we have a speed back and so breaking this up into the two equations our speed on the way there is going to be 45 times the time of t is equal to the distance, right, the distance to the airport.
03:40
And the return trip is going to be the same process as well.
04:05
So we've got that for the first expression.
04:08
And then the second expression is going to be the distance will be equal to the speed of the return trip, which would be equal to 30...