Two carts, A and B, are connected by a rope 28 ft long that passes over a pulley P (see the figure). The point Q lies 12 ft directly below P at the same height at which the ropes are attached to the carts. Cart A is being pulled away from Q at the rate of 2 feet per second. How fast is cart B moving towards Q at the instant when cart A is 9 ft away from Q?
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