Question

I have three questions... (copied below)

Answer 1

-The two situations; one situation where Beth is correct and a separate situation where Kelly is correct, can be:
sqrt(x) = -2  and   sqrt(x) = 2

- For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix. So by definition, if you create a parabola for the focus (the rock) and define the fence as the "line not through the focus" that is:
y = (1/4f)*x^2 where f is 1/2 perpendicular distance from the rock to the fence. 

-Allen can complete 1/16 of the project per hour Brianne can complete 1/18 of the project per hour Charles can complete 1/x Together they can accomplish 1/16 + 1/18 + 1/X per hour. we need a common denominator, which is

288X = 18x+16x+288288x
Choose t as the time it takes them all, so 1/t is the hourly rate.
 
1/t =18x+16x+288288x
or
t =288x18x+16x+288

Once the project is completed, Jocelyn will have t, so she will only need to solve for x in this equation to find out the rate 1/x for Charles working by himself