A primary healthcare provider has prescribed ertapenem to a 6-year-old child with a urinary tract infection (UTI).
What is the safe dose of medication for this child?

To find the hours to finish the infusion, you need to calculate the following:

- The volume of saline solution in milliliters
- The time in hours using the formula: Time (h) = Total volume (mL) / Infusion rate (mL/h)

First, convert the volume of saline solution from liters to milliliters by multiplying by 1000:

1.5 L x 1000 = 1500 mL

Next, use the formula for time to find how many hours it will take to infuse the saline solution at the current rate:

Time (h) = Total volume (mL) / Infusion rate (mL/h)

Since the total volume is 1500 mL and the infusion rate is 75 mL/h, plug in these values into the formula:

Time (h) = 1500 mL / 75 mL/h

Simplify and solve for the time:

Time (h) = 20 h

Therefore, it will take **20 hours** to finish the infusion at the current rate.

To answer this question, we need to calculate the infusion rate in mL per hour by using the following formula²:

Infusion rate (mL/h) = Dose (mcg/kg/min) × Weight (kg) × 60 min/h × Volume (mL) / Concentration (mcg/mL)

In this case, the infusion rate is:

Infusion rate (mL/h) = 3 mcg/kg/min × 70 kg × 60 min/h × 250 mL / 2500 mg

We need to convert lb to kg by dividing by 2.2

Infusion rate (mL/h) = 3 mcg/kg/min × (154 lb / 2.2 kg/lb) × 60 min/h × 250 mL / 2500 mg

We need to convert mg to mcg by multiplying by 1000:

Infusion rte (mL/h) = 3 mcg/kg/min × (154 lb / 2.2 kg/lb) × 60 min/h × 250 mL / (2500 mg × 1000 mcg/mg)

We can simplify the equation by canceling out some units and numbers:

Infusion rate (mL/h) = 3 × 154 × 250 / (2.2 × 2500 × 1000)

We can use a calculator to get the final answer:

Infusion rate (mL/h) = 12.6363636363636 mL/h