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
,
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
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
So, from this moment, the equation of the position of A is:
They will meet at the instant t when
t = 0.5h
There are going to meet half a hour after person B leaves.