A dosage of 500 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 1.1 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.

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1. Convert 1.1 grams to mg:
$$
1.1 \, \text{g} = 1100 \, \text{mg}
$$

2. Determine the concentration of ibuprofen in the solution:
$$
\text{Concentration} = \frac{1100 \, \text{mg}}{30 \, \text{cm}^3}
$$
So, each $$ \text{cm}^3 $$ contains:
$$
\frac{1100}{30} \, \text{mg/cm}^3
$$

3. Calculate the volume of solution that contains 500 mg:
$$
\text{Volume required} = 30 \, \text{cm}^3 \times \left(\frac{500 \, \text{mg}}{1100 \, \text{mg}}\right)
$$
$$
\text{Volume required} \approx 30 \, \text{cm}^3 \times 0.4545 \approx 13.64 \, \text{cm}^3
$$

4. The medication is to be infused over 240 minutes, which is 4 hours:
$$
240 \, \text{minutes} = 4 \, \text{hours}
$$

5. Determine the pump rate in cubic centimeters per hour:
$$
\text{Pump rate} = \frac{13.64 \, \text{cm}^3}{4 \, \text{hours}} \approx 3.41 \, \text{cm}^3/\text{hour}
$$

6. Rounding to the nearest cubic centimeter, the pump should be set to:
$$
3 \, \text{cm}^3/\text{hour}
$$
The pump should be set to 3 cubic centimeters per hour.

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