Question

"You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the restaurant is given by y=−40x+200, where x is the number of hours since your friend left home. You live 100 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant."

Answer 1

The equation will be:

$y=-20x+100$

Why?

Let's work with your friend equation in order to find the time from his house to the restaurant (is the same as yours).

We are given the following function:

$y=-40x+200$

When: $y=0$ our friend arrived, so, calculating "x", we have:

$0=-40x+200\\\\40x=200\\\\x=\frac{200}{40}=5h$

We have that it took 5 hours for our friend to arrive at the restaurant, and it's the same time for you. We know that you live 100 miles from the restaurant.

Your equation will have the following form:

$y=-k*x+distance$

Where,

y is the position

k is the rate distance/time

x is the time

Now, again, when $y=0$, you will have arrived at the restaurant too, so:

$0=-k*x+100$

Using "x" equal to 5 hours, because you will have arrived at that time too, we have:

$0=-k*5+100\\\\k=\frac{100}{5}=20$

Your equation will be:

$y=-20x+100$

Have a nice day!