00:01
In this question, we have two people leaving from the same place.
00:05
Lois leaves at 8 a .m.
00:07
And travels at 35 miles per hour.
00:09
Clark leaves at 8 .15 a .m.
00:12
And travels at 40 miles per hour.
00:14
And the question is, at what time will they be 140 miles apart? so the first part that we need to address is in this 15 minute gap from 8 a .m.
00:28
To 8 .5.
00:28
15 a .m.
00:30
How far does lois travel? this way we know how far ahead or what head start lois has.
00:38
And so to find this out, we have 15 minutes, which is the same thing as one fourth hour.
00:47
And if we multiply this by lois's speed of 35 miles per hour, we'll get how far he traveled, which turns out to be 8 .75 miles.
00:58
And so lois has an 8 .7 .5 miles.
00:58
And so lois has an 8 .5.
01:01
5 .75 mile head start over clark.
01:06
And so to solve this problem, let's go ahead and write an expression representing the distance traveled for each of them.
01:12
So for lois, he's traveling at 35 miles per hour times x hours.
01:20
And we're going to add the head start that he has.
01:24
Then for clark, he simply is traveling at 40 miles per hour times x hours.
01:31
And so each of these represented the distance, each of them travel in x hours.
01:38
So to start, lois has a 8 .75 mile head start, which is obviously not 140 miles.
01:47
And since clark, his speed is faster than lois's, we know that this 140 miles will happen when clark is 140 miles ahead of lois.
01:59
And so to solve this, we're going to set up an equation.
02:04
We're going to have the distance of clark travels, which is 40x, and we're going to subtract it by the distance lowest travels, which is 35x plus 8 .75.
02:15
And this is going to equal 140, because we want to know when clark is 140 miles ahead...