SOLUTION: Please help me to solve this word problem. We have just started this new section and I just can't solve it. Water from a fire hose is sprayed on a fire that is coming from a

Question 305737: Please help me to solve this word problem. We have just started this new section and I just can't solve it.
Water from a fire hose is sprayed on a fire that is coming from a window. The window is 15m up the side of a wall. The equation H=-0.011x^2+.99x +1.6 models the height of the jet of water, H, and the horizontal distance it can travel form the nozzle, x, both in meters. What is the maximum height that the water can reach? and how far back could a firefighter stand, but still have the water reach the window?
Found 2 solutions by nerdybill, richwmiller:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Water from a fire hose is sprayed on a fire that is coming from a window. The window is 15m up the side of a wall. The equation H=-0.011x^2+.99x +1.6 models the height of the jet of water, H, and the horizontal distance it can travel form the nozzle, x, both in meters. What is the maximum height that the water can reach? and how far back could a firefighter stand, but still have the water reach the window?
.
The given equation:
H=-0.011x^2+.99x +1.6
Is a parabola that opens downwards.
.
What is the maximum height that the water can reach?
This entails finding the vertex.
Axis of symmetry = -b/(2a) = -.99/(2*(-0.011))
Axis of symmetry = .99/0.022
Axis of symmetry = 45 meters
.
H=-0.011x^2+.99x +1.6
H=-0.011(45^2)+.99(45) +1.6
H= 23.875 meters (maximum height)
.
Distance from wall:
45 meters

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
The other tutor got the height right.
But to hit the 15m window we set h=15
we get two usable answers
(x-73.4045) (x-16.5955) = 0
x-73.4045
x=16.5955
The answer the other tutor gave would have the water go to high.
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