# Calculus

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Two cars start moving from the same point. One travels south at 60 mph and the other travels west at 25 mph. At what rate is the distance between the cars increasing 2 hours later?

Let x = the distance covered by the south traveling car.
Let y = the distance covered by the west traveling car.
Let z = the distance between the cars.

In this problem you are given two rates. What are they? Express your answers in the form dx/dt, dy/dt, or dz/dt = a number. Enter your answers in the order of the variables shown; that is, dx/dt first, dy/dt, etc. next.

What rate are you trying to find?

Write an equation relating x and y . Note: In order for WeBWorK to check your answer you will need to write your equation so that it has no denominators. For example, an equation of the form 2/x = 6/y should be entered as 6x=2y or y = 3x or even y - 3x = 0.

Use the chain rule to differentiate this equation and then solve for the unknown rate, leaving your answer in equation form.

Substitute the given information into this equation and find the unknown rate. Express your answer in the form dx/dt or dy/dt = a number.

• Calculus -

x = 60t
y = 25t
z = √(x^2+y^2) = 65t

All that chain rule stuff is irrelevant here, since dz/dt = a constant.

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