Question

A healthcare worker expected to give medication dosage to 80 patients. However, one day she took 4 hours longer than expected, resulting in giving medication to 10 patients less per hour. How long did she expect to give medication dosage to 80 patients?

a) 6 hours
b) 8 hours
c) 10 hours
d) 12 hours

Answer 1

The healthcare worker was expected to give medication dosage to 80 patients in 2.5 hours.

Step-by-step explanation:

To find out how long the healthcare worker expected to give medication dosage to 80 patients, we need to determine the time it takes for the healthcare worker to give medication to one patient. Let's assume the expected time to give medication to one patient is X hours. Since the healthcare worker took 4 hours longer than expected, the actual time it took to give medication to one patient is X + 4 hours. Additionally, since the healthcare worker gave medication to 10 patients less per hour than expected, the actual time it took to give medication to one patient is (X + 4) + 10/X hours. To find X, we can set up an equation:

X = (X + 4) + 10/X

Simplifying the equation:

X^2 = X (X + 4) + 10

X^2 = X^2 + 4X + 10

Subtracting X^2 from both sides:

0 = 4X + 10

Subtracting 10 from both sides:

-10 = 4X

Dividing both sides by 4:

X = -10/4

X = -2.5

Since time cannot be negative, the expected time to give medication dosage to 80 patients is 2.5 hours.