Monique and tasha are traveling on the same highway to a family reunion at a park. monique starts out 225 miles from the park and drives 70 miles per hour. tasha starts out 200 miles from the park and drives 65 miles per hour. will monique's and tasha's trip overlap before they reach the park? explain your reasoning.

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

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

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

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.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.