  We study the velocity of travelling waves of a reaction-diffusion system
coupling a standard reaction-diffusion equation in a strip with a
one-dimensional diffusion equation on a line. We show that it grows like the
square root of the diffusivity on the line. This generalises a result of
Berestycki, Roquejoffre and Rossi in the context of Fisher-KPP propagation
where the question could be reduced to algebraic computations. Thus, our work
shows that this phenomenon is a robust one. The ratio between the asymptotic
velocity and the square root of the diffusivity on the line is characterised as
the unique admissible velocity for fronts of an hypoelliptic system, which is
shown to admit a travelling wave profile.
