Express the distance $\"\"$ between the cars as a function of the time $\"\"$ .

At $\"\"$ , the cars leave the intersection.

One is headed south at a constant speed of $\"\"$ miles per hour, and the other is headed west at a constant speed of $\"\"$ miles per hour.

If $\"\"$ is in hours, $\"\"$ is the distance traveled with speed of $\"\"$ mph at time $\"\"$ .

$\"\"$ is the distance traveled with speed of $\"\"$ mph at time $\"\"$ .

Observe the figure, hypotenuse is $\"\"$ and $\"\"$ .

Apply Pythagorean theorem, $\"\"$ .

$\"\"$

$\"\"$ .