Basic Math Question for Health Care

Question

This is super basic, but I have not been in school for YEARS. I am a bit dusty. Any-who, Its a common word problem, and as follows: A licensed practical nurse gives 1800 milligrams of penicillin over a 36 hour time period. If the dosage occurs every 6 hours, how many milligrams are in each dose if the dose is the same amount each time?

Answer 1

So we divide 36 by 6 to get the number of doses the nurse gives which is 6. We then divide the mass of penicillin by the number of doses the nurse gave. So 1800/6=300 milligrams.

So therefore there are 300 milligrams of penicillin in each dose.

Answer 2

Problems like these are prone to the so-called "off-by-one" or "fencepost error", which you can read about, e.g., here: https://en.wikipedia.org/wiki/Off-by-one_error

To avoid it, you have to be very clear what you mean.

My reading of this question would be this: let's pick a start time: Midnight Sunday morning, say, for the first dose. Last dose is $36$ hours later, at noon on Monday. The full list of doses given is:

$$\{12\; AM, 6\; AM, 12\; PM, 6\; PM, 12\;AM, 6\;AM, 12\;PM\}$$

Hence, $7$ doses all in all. Assuming this is what is intended, the answer would then be $$\frac {1800}{7}\;\sim\;257.143$$