Precalculus problem

Question

You and a friend live 4 miles apart (on the same "east-west" street) and are talking on the phone. You hear thunder produced by lightning in a storm, and 18 seconds later your friend hears the thunder. Find an equation that gives the possible places where the lightning could have occurred. (He assumes that the coordinate system is measured in feet and that sound travels at 1100 feet per second.)

i'm not really sure how to solve this problem, please help

Answer 1

Draw and label a daigram on a Cartesian plane

You are at (0, 0), your friend at (21120, 0)

The lightening bolt is at (x, y).

The distance from you to the bolt is 1100s feet

The distance from your fried to the bolt is 1100(s + 18)

By Pythagoras:

x² + y² = (1100s)²

(21120 - x)² + y² = 1100(s + 18)

Solve for equations for y²

Set sides equal and solve for x.

Use x to determine y.