A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (the figure). The waves are of two types: transverse waves traveling at v_t = 56 m/s and longitudinal waves traveling at v_l = 166 m/s . If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference Δt in the arrival times of the waves at its leg nearest the beetle. If Δt = 4.6 ms, what is the beetle's distance?