No need for "double tracks in each direction.
A  6:03 train bypasses station #1 and stops at #2, #4, 6 # 8 etc.
A 6:06 train at #1, #3, # 5, #7, #8 and bypasses even numbered stations
The 6:06 train running behind the 6:03 would be incapable of overtaking the 6:03 because both trains make the same number of stops and run at the same speed.