Equation linking BAC (blood alcohol concentration) and Time?

Question

A man starts at 6pm drinking 3 per hour. His BAC increases by 0.017 per drink. what would the equation linking his BAC and time be? And a ladies BAC is 0.085 at midnight it decreases by 0.012 per hour. What is the equation linking her BAC and time?

i can't work it out

Answer 1

Let t be hours since midday.
Then the man's BAC increases by 3×0.017 = 0.051 per hour, so the equation is
BAC = 0.051 (t-6)
The (t-6) reflects the fact that he starts drinking at 6 pm, so at this point his BAC is 0.

Similarly, the woman's BAC decreases by 0.012 per hour and starts off at 0.085 at t=12, so we get
BAC = 0.085 - 0.012 (t - 12).

Answer 2

Bac Equation