SOLUTION: From Glencoe Alg I 10-4 #4 word problem. I have spent over a day with this one. Firefighting. Firefighters calculate the flow rate of water out of a particular hydrant by the f

Question 959333: From Glencoe Alg I 10-4 #4 word problem. I have spent over a day with this one.
Firefighting. Firefighters calculate the flow rate of water out of a particular hydrant by the following formula: Flow rate = 26.9 x d^2 x sqrt P. P is nozzle pressure and d is hose diameter. The combined flow rate of two hoses is 2430 gpm. The diameter of each hose is 3 inches but the pressure of one hose is 4 times that of the other. What are the nozzle pressures of each hose?
I have the answer key and it says 11.2 and 44.8 psi. For the life of me, regardless of how I manipulate the formula, I cannot come up with this answer.Can you show me the setup of the formula?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The problem uses the following formula
Flow rate = 26.9 x d^2 x sqrt P
we have two hoses with d = 3 each and P and 4p for pressure, therefore we have the following formula
(26.9 * 3^2 * sqrt(P)) + (26.9 * 3^2 * sqrt(4P)) = 2430
(242.1*sqrt(P)) + (242.1 * sqrt(4P)) = 2430
Note that sqrt(4P) = 2*sqrt(P)
(242.1 * sqrt(P)) + (484.2 * sqrt(P)) = 2430
726.3 * sqrt(P) = 2430
sqrt(P) = 3.345724907
square both sides of =
P = 11.193875154 approx 11.2
The two pressure values are 11.2 psi and 44.8 psi

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