### Home > CALC > Chapter 7 > Lesson 7.1.4 > Problem 7-43

7-43.

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 the eastbound car leaves? Homework Help ✎

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.

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

Evaluate.

≈ 48.788 mph