Particle Boom

Three particles, say $X,Y,$ and $Z$ , start at integer positions $x < y < z$ , where $x,y,$ and $z$ have the same parity. The three particles perform independent simple symmetric random walks on the integers. This means that each particle moves $\pm 1$ with equal probability each minute, independently of the other particles. Find the expected number of minutes until there is a collision between particles when $x = 10, y = 20,$ and $z = 40$ .

Answer format: enter an integer.