# Related rates

Two carts A and B are connected by a rope 39 feet long that passes over pulley P. The point Q is on the floor directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 2 ft/sec. How fast is cart B moving toward Q at the instant cart A is 5 feet from Q?

Express solution using related rate notation i.e. dy/dt or dx/dt

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#### Solution Preview

We need one more piece of information to answer this question - the height of the pulley. Call this h. Let a be the distance from Cart A to Q and b be the distance from Cart B to Q. Let x be the length of rope from P to A and let y be the length from P to B. Let the length of the rope be L. Hopefully, you are drawing a picture as we go and you should have two right angle triangles which ...

#### Solution Summary

This shows how to work with related rates in a word problem.