Answer:
There are going to meet half a hour after person B leaves.
Step-by-step explanation:
The first step to solve this problem is model the position equation for both person A and person B. It can be done by a first order equation.
I am going to say that the positive direction is from the person A to the person B. So, A starts at the position 0 and B at the position 76.
The first step is to find the equation of the position of person A
The initial position of A is 0 and he travels 44 miles per hour in the direction of B, so to the positive diretion. So, the position S of person A is
[tex]S_{A}(t) = 44t[/tex],
where t is the time in hours.
Now we have to find the equation of the position of person B
The initial position of B is 76 and he travels 64 miles per hour in the direction A, so in the negative direction. The position S of person B is
[tex]S_{B}(t) = 76 - 64t[/tex]
Now we have to restart the time from the moment the person B leaves her house.
It happens at 0.5h, at this moment the person A is at the position
[tex]S_{A}(0.5) = 44*(0.5) = 22[/tex]
So, from this moment, the equation of the position of A is:
[tex]S_{A}(t) = 22 + 44t[/tex]
They will meet at the instant t when
[tex]S_{A}(t) = S_{B}(t)[/tex]
[tex]22 + 44t = 76 - 64t[/tex]
[tex]108t = 54[/tex]
t = 0.5h
There are going to meet half a hour after person B leaves.
