Answer:
They don't overlap at any point.
Step-by-step explanation:
The easiest to solve this problem is by find the linear expression for both cases, graph them and see if their lines intercept at some point.
Monique.
According to the problem, Monique starts at 225 miles from the park, this is an initial condition, so it's gonna be the independent term. She travels at a rate of 70 miles per hour, this is gonna be the coefficient of the variables, because ratio refers to the slope. So, Monique's expression would be
[tex]y=-70x+225[/tex]
Tasha.
We do the same process for Tasha. She starts at 200 miles from the part, and she travels with a ratio of 65 miles per hour. So, the linear expression would be
[tex]y=-65x+200[/tex]
Now, the graph attached shows both lines. From the image you can tell that lines don't intercept each other, this means that they don't overlap during the travel. In case that they overlap, both lines should intercept each other near to the x-axis, which represents the final point.
Another way to see if they overlap is by solving the system of equations
[tex]\left \{ {{y=-70x+225} \atop {y=-65x+200}} \right. \\\left \{ {{-y=-70x-225} \atop {y=-65x+200}} \right. \\0=-135x-25\\-135x=-25\\x=\frac{-25}{-135}=0.18[/tex]
Using the graph, you can see that this interception coordinate is place on the negative side of the y-axis, which doesn't make sense with the problem. So, they don't intercept before their destination.
