If he fires a bullet in the same direction as the direction that the horse is running, the total speed of the bullet is the sum of the speed the bullet was propelled out of the gun plus the speed of the horse, for a combined speed of 400+20=<<400+20=420>>420 feet per second.
If he fires a bullet in the opposite direction as the direction in which the horse is running, then the total speed of the bullet is the speed the bullet was propelled out of the gun minus the speed of the horse, for a resulting speed of 400-20=<<400-20=380>>380 feet per second.
Thus, when firing the gun in the same direction as the horse is running, the bullet moves at 420-380=<<420-380=40>>40 feet per second faster than when he fires the bullet in the opposite direction as what the horse is running.
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