First step was to equate the goal amount in terms of no. of car jobs and refueling costs
NOTE: A/B would be A divided by B
Goal amount = (no. of car jobs x 50) - ((no. of car jobs / 30) x 150) (Approximations here are:
50g for each car job and
30 car jobs until full tank refuel with
150g for full tank refuel)
NOTE: I will use algebra from now when there are no new terms to keep it simpler (sorry to the guys who can't do maths)
eg for the line above it would be:
G = 50n - (n / 30) x 150
Next steps were simplifying the goal amount equation
G = 50n - 5n
G = 45n
n = G/45
Now I made a new part of the formula for the time taken which I will combine later to the one above
The plain English start of this equation is:
Time taken = (no. of car jobs x no. of hours taken for the job) + (no. of car jobs x no. of hours taken to get the mission) + ((no. of car jobs / car jobs until full refuel) x no. of hours taken to refuel)
Which in algebraic terms would be:
T = (n x 1/60) + (n x 1/120) + (n/30 x 1/180) (Approximations being
1 min for doing the job,
1/2 min for getting the mission and
1/3 min refueling)
Again, I simplify the equation
T = n/60 + n/120 + n/5400
T= 17n/675
Now that I have both parts, I can combine them together by substituting n= G/45 (which I got above) into the equation directly above this
T = (17 x G/45) / 675 (the first part in brackets is supposed to be on top of 675 just if it wasn't clear)
T= (17G / 45) / 675
T= 17G / 30375
And there you have it!!!
The steps on how I derived this equation!!! Again, feel free to fix up any approximations you think are incorrect!!!