Question 1092324
.

{{{graph( 330, 330, -15.5, 10.5, -20.5, 20.5,
          -x^2-4x, -3x^2-15x
)}}}


Plot y = {{{-x^2-4x}}} (red) and y = {{{-3x^2-15x}}} (green)


<pre>
This plot is to illustrate the problem.


You have two jets released from the origin (0,0).

They intersect somewhere. You need to find the intersection point.


For it, since "y"-s are equal, you can equate the right sides:


-x^2-4x = -3x^2-15x.


Which implies

2x^2 + 11x = 0  ====>  x*(2x + 11) = 0. ====>

====>  the only interesting root is 2x + 11 = 0,  i.e.  x = {{{-11/2}}}.


Then y = {{{-(-11/2)^2 - 4*(-(11/2))}}} = -8.25.


<U>Answer</U>.  The vertical height difference, d, of the pools is 8.25 ft.
</pre>

Solved.