Problem

A dosage of $600 \mathrm{mg}$ of ibuprofen is to be delivered to a patient in an IV drip over 240 minutes. It's supplied in a solution that contains 1.3 grams of the drug in $30 \mathrm{~cm}^{3}$ of the solution. The pump used to deliver the drug uses units of cc's (cubic centimeters) per hour. At what rate should the pump be set? Round your answer to the nearest cubic centimeter. The pump should be set at a rate of cc per hour.

Solution

Step 1 :Convert the dosage from mg to g: \(600 mg = 0.6 g\)

Step 2 :Find out how many cm³ of the solution contains the required dosage: \(0.6 g / 0.043333333333333335 g/cm³ = 13.846153846153845 cm³\)

Step 3 :Convert the time from minutes to hours: \(240 minutes = 4.0 hours\)

Step 4 :Calculate the pump rate by dividing the volume of the solution by the time in hours: \(13.846153846153845 cm³ / 4.0 hours = 3.4615384615384612 cm³/hour\)

Step 5 :Round the pump rate to the nearest cubic centimeter: \(round(3.4615384615384612) = 3\)

Step 6 :Final Answer: The pump should be set at a rate of \(\boxed{3}\) cc per hour.

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Source: https://solvelyapp.com/problems/19609/

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