A 52 kilogram male is admitted to the emergency department with
uncontrollable asthma. The Doctor orders an aminophylline infusion at
a dose of 0.3 milligrams per kilogram per hour. If the infusion
solution is 500 milligram in 250 mls, what will the rate of the pump
be set at in mls per hour.

Hello.

If the dose is 0.3 milligrams per kilogram per hour, then the patient
should receive 15.6 milligrams total per hour because he weighs 52
kilograms.

52 kg * 0.3 mg/kg/hr = 15.6 mg/hr

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If the infusion solution is 500 milligram in 250 mls, then there are 2
milligrams in every milliliter.

500 mg / 250 ml = 2 mg/ml

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If there are 2 milligrams per milliter, the patient would need 7.8
milliliters to receive 15.6 milligrams.

15.6 mg/hr / 2 mg/ml = 7.8 ml per hour

Thus, that's the answer.  The pump should be set at 7.8 ml per hour.

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I hope this helps.