Dimensional Analysis - Complex

1. Units and Conversion 1.6) Dimensional Analysis 1.6.1) Dimensional Analysis

1.6.1.1) Dimensional Analysis Hard 1


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A 182 lb patient is taking a chemo drug costing 46.12 cent per mg. The recommended dose is 3.78 mg per kg of body weight. The nurse is administering a solution of 0.54 mg/mL concentration and the pump is infusing it at the rate of 1.1 mL/min. The tubing of this particular pump delivers 17 gtt/mL.

How long did it take for the patient to complete the infusion, in minutes?


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lb equals 526.45 kg

    • This problem has the following paired information:
      46.12 cent = 1 mg drug
      0.54 mg drug = 1 mL solution
      3.78 mg drug = 1 kg body weight
      1.1 ml solution = 1 min
      17 drops = 1 mL solution
      patient's body weight = 182 lb
      Also, you need to know that 1 kg = 2.2 lb.

    Since this problem is asking the time in minutes unit, we have to take the relationship where min unit is present. Hence, we take 1.1 mL/min and flip and use as the first fraction.
    1 min × 1 mL × 3.78 mg × 182 lb × 1 Kg
    1.1 mL 0.54 mg 1 Kg 1 2.2 lb

    Therefore, the total time is 526.45 minutes. Ans.