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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