Juntion box wire optimization

[hawt_tacos]

Homework Statement

Two isolated farms are 12km apart on a straight country road that runs parallel to the main highway 20km away. The power company decides to run a wire from the highway to the junction box, and from there, wired of equal length to two houses. Where should the junction box be placed to minimize the length of wire needed

Homework Equations

[(x2-x1)^2+(y2-y1)^2]^0.5=D

The Attempt at a Solution

I split the distance between the farms in half and used the midpoint as (0,0)

I set the juntion box as (x,0) and one farm house as (0,6)

putting those into the distance formula I got D=[x^2+36]^0.5

taking the derivative of D^2 i get 2x, setting it to 0=2x gives me x=0. a numberline test shows 0 is a min value

after that I put the 0 back in my origiinal D equation which gave me a distance of 6km, however this answer feels wrong since the box would be 20km from the main road. feedback is appreciated

 

[Dick]

I think they want you to minimize the length of ALL of the wire used. Not just the wire connecting the one house to the junction box. Try minimizing (20-x)+2*[x^2+36]^0.5.

 

[hawt_tacos]

annddd that would make more sense, thanks. I was hoping to get a distance and solve using pythagorean, but looking at what you did that would be the wrong direction.