Two cars, A and B, are connected by a rope 39 feet long that passes over a pulley P. The point Q is on the floor 12 ft directly beneath P and between the cars. Cart A is being pulled away from Q at a sped of 2 ft/s. How fast is cart B moving toward Q at the instant when cart A is 5 ft from Q?

P distance from P to Q is 12 ft.

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A Q B

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I was able to use pythagorus to find the lengths of AP and PB when AQ=5 but and got 13 and 26 respectively.

Let BQ=x and PQ=y and PB=z

x^2 + y^2 = z^2

2x dx/dt + 2y dy/dt = 2z dz/dt

We know

x=2root133

y=12

z=26

dy/dt=0

dx/dt= what we're solving for

but what about dz/dt?

Am I missing a step? Where did I go wrong?