You have four loads drawing 160 mA each, for a total of 640 mA. You have a battery pack rated for 15 Ah. Both the battery and load work at the same voltage.
(15 Ah)/(640 mA) = 23.4 hours
Yes, the math really is that simple.
However, batteries are a lot more complicated than just a single charge capacity rating. The battery capacity changes with temperature, previous history, rate of discharge, phase of the moon, and what your dog had for lunch yesterday.
Take the math as a rough guide. The answer is therefore "not quite a day".
If you have to give a minimum guaranteed spec to a customer, you should derate heavily. You should also do a few real tests then. Make sure the fans really do only draw 640 mA or less, and that the battery pack really can put out 15 Ah before the voltage goes too low to be useful. If everything is working correctly, you might specify 20 hours at room temperature. Derating by half in a more general case isn't out of line at all.