The units of [tex]r'(t)[/tex] are gallons per square hour.
Dimensionally speaking, [tex]r(t)[/tex], expressed in gallons per hour, is length raised to third power divided by time. Capacity units are volume units.
As rate of change represents the instantaneous change of [tex]r(t)[/tex] in time, then we find that units are length raised to third power divided by time raised to second power.
Hence, the units of [tex]r'(t)[/tex] are gallons per square hour.
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