Question

Please. I need help, otherwise I will fail, because I need to know how to do this!
A gas line from two different houses need to join up at a coupler unit under the street in front of the houses. In order to minimize the amount of piping needed, where should the gas lines intersect the main line out in the street?

I have posted the picture below.

Answer 1

Here is the picture of it.

Answer 2

Refer to the attached solution using the Mathematica 9 computer program.

Answer 3

Thank you for your help! However, I'm in precalculus and we haven't learned derivatives. Do you know how to solve it another way?

Answer 4

Beats me. Now you see the power of the calculus.
The attached plot will put you in the ball park.
Also "a" happens to be an integer.
Leaves trial and error I guess.

Answer 5

Thank you for the medal.

Answer 6

Okay, thank you for trying!

Answer 7

The shortest distance is when B is located such that A'BC is a straight line, which translates to triangles ADE and CEB are similar.
Thus by proportion,
mDB/mDA = mBE/mCE
Solve for DB (knowing mDB+mBE=120).