My question is, "Under these circumstances, can I expect the battery to
last for the more or less 18 hours that I will be operating?" 

Obviosuly, if not, buying a second battery is a not-very-expensive option.  

Randy W6SJ

The Amp Hour rating tells you how much amperage is available when discharged
evenly over a 20 hour period. The amp hour rating is cumulative, so in order
to know how many constant amps the battery will output for 20 hours, you
have to divide the amp hour rating by 20. Example: If a battery has an amp
hour rating of 75, dividing by 20 = 3.75. Such a battery can carry a 3.75
amp load for 20 hours before dropping to 10.5 volts. (10.5 volts is the
fully discharged level, at which point the battery needs to be recharged.) A
battery with an amp hour rating of 55 will carry a 2.75 amp load for 20
hours before dropping to 10.5 volts.

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