A pump removes water from a flooded basement at a time–dependent rate modeled by r(t)=0.5+0.02t,0≤t≤60, where r(t) is measured in gallons per minute and t is the time in minutes after the pump is turned on.
(a) Calculate the average rate at which the pump removes water during the first 60 minutes. Express your answer with appropriate units.
(b) Determine the total number of gallons pumped out during this time period.
(c) Local regulations stipulate that the average pumping rate must not exceed 1.1 gallons per minute over any 60-minute interval. State whether the pump meets this requirement and justify your conclusion numerically.