Intermediate Value Theorem Word Problem

[harrietstowe]

Homework Statement

The image can be seen at:
http://s1130.photobucket.com/albums/m521/harrietstowe/?action=view&current=photo1.jpg

The rectangle in the picture represents the floor of a room and AB a straight piece of string lying on the floor whose ends touch the opposite walls w1 and w2. The blob is the same string tangled up. I need to show that there is at least one point of the tangled string whose distances from the two walls are exactly the same as they were before.

Homework Equations

The Attempt at a Solution

I tried to graph the situation by saying the regular string is f(x) and the tangled string is g(x) and then graphing h(x)=f(x)-g(x) but I am now stuck.
Thank You

 

[LCKurtz]

Think about the straight string of length L with x coordinate parameterized by arc length s so its x coordinate is f(s) = s, 0 ≤ s ≤ L. Then think of the tangled string still parameterized by s so

R(s) = < x(s), y(s) >, 0 ≤ s ≤ L

Then look at f(s) - x(s) and see what you come up with.