CPM Homework Help : CALC3RD Problem 7-40

Two roads intersect at right angles. Elizabeth, who is driving east, leaves the intersection traveling at a speed of $40$ mph. Two hours later, Nairi leaves the same intersection at a speed of $30$ mph heading north. How fast is the distance between the cars changing five hours after Elizabeth leaves?

Hint:

Let the eastbound car be at a distance $x$ from the intersection and the northbound car at distance y.
Write an equation for the distance between them.

Step 1:

$\text{Then the distance between them is }\sqrt{x^{2}+y^{2}}.$

Step 2:

Implicitly differentiate the distance equation with respect to time. This will create a rate equation.

Step 3:

Evaluate.

Answer:

$≈ 48.788$ mph