If we know the volumetric flow rates of the water going into the two branches, then what would be the velocity of the water coming out?

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noone is correct you should apply floyds equations to calculate the velocity, you cannot solve that with the parameters they gave to us.

quantity water =area*velocity

Q=AV which yields 247.6 in/s

Elizabeth is correct.

Richard, v1a1 = 7000 in^3 = v2a2. You just divide 7000 by A2 to get v2. A2 = 9*pi

247.6 in/s

Isnt the answer 2 x 247.6 = 495.13

Because v1a1 = v2a2

Q=AV which yields 247.6 in/s

247.6 in/s