There's no mention of actual distance, only of actual rates. That means we can't determine actual total time, which rules out (B).

Let's say actual total distance = 360.

Distance traveled at 20mph $= \frac{1}{3} * 360 = 120$
1/2 the remaining distance $\frac{1}{2} * (360 - 120) = 120$
The remaining distance $= 360 - (120+120) = 120$

Let a = Time taken to travel the part of the distance at 20 mph, b = Time taken to travel the part of the distance at 12 mph, and c = Time taken to travel the part of the distance at 40 mph.

Using the distance-rate formula, t = d/r :
$a = 120 / 20 = 6$
$b = 120 / 36 = \frac{10}{3}$
$c = 120 / 40 = 3$

Since c = 1/2a, (A) is correct.

The average speed for the entire journey = $\frac{360}{6 + \frac{10}{3} + 3} = 18.95$, so (C) is incorrect.