The closer the zombies are to you, the higher the chance you can get a headshot with the pistol, which will instantly kill it. You can increase the chance of a headshot by upgrading the pistol at the armory on the main menu. It costs rations to upgrade your weapons. After reaching classroom 3, you will have access to the shotgun. It will result in a headshot on all three zombies when fired at them directly behind you. Save the shotgun for emergency situations.