Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3.5 ft/s. How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q? (Round your answer to two decimal places.)

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1. looking at a diagram, if A is a away from Q and B is b away from Q, then

√(a^2+144) + √(b^2+144) = 39
a/√(a^2+144) da/dt + b/√(b^2+144) db/dt = 0

Now just plug in
da/dt = 3.5
a = 5
b = 23.065 (from 1st equation when a=5)

and solve for db/dt

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