Question 180862
v = volume of tank
r = miles per gallon

distance = vr

dr/dv = -0.5  (every increase of 2 decreases by 1)

r = c - 0.5v (integrate)

22 = c - 6 (substitute r=22,v=12)

c = 28

v(28-0.5v) = distance (substitute)

28-0.5v -0.5v = 28-v = 0 (differentiate and solve for turning point)

v = 28 

r = 28 - 14 = 14 (calculate r at turning point)

14*28 = 392 (calculate distance)