What is the Distribution of an Ambulance's Distance from an Accident on a Road?

[dashkin111]

Homework Statement

An ambulance travels back and forth, at a constant speed, along a road of length
L. At a certain moment of time an accident occurs at a point uniformly distributed on the
road. (That is, its distance from one of the fixed ends of the road is uniformly distributed
over (0,L).) Assuming that the ambulance's location at the moment of the accident is also
uniformly distributed, compute, assuming independence, the distribution of its distance from
the accident.

Homework Equations

The Attempt at a Solution

Using X = ambulance position, Y = accident position I found

fx(x) = 1/L for x<= L
fy(y) = 1/L for y<=L

Now I'm stuck. :(

 

[dashkin111]

So am I right thinking we have to find:

f|x-y|(x-y)?

 

[dashkin111]

Last bump, I hope someone can help me this time!