The embankment fill is specified to be 90% of the Modified Proctor maximum dry density, so the weight of DRY soil required is a straightforward calculation... do you follow that?
Knowing the dry weight of the soil required, you can ignore the contribution of the water weight - all you care about it the amount (by weight) of dry soil in the truck. Granted, the soil will contain water (16%) but it doesn't change the weight of the dry soil for the given volume. If there was a weight limit given for the truck, then you'd have to verify the water weight doesn't create a limiting factor (which should still be unlikely).
So, all you need to do is figure out the dry weight of the soil that gets put into the truck. Water fills the space between soil particles (until it's saturated - not the case here) and doesn't "take away" from the truck volume capacity.
I hope I've explained this good... the moral of the story is that problems often give you more information than you need to solve the problem. In this case, moisture information is there just to confuse you!
P.S. I wish someone would put some geotech info on the
PE Notes wiki - I think a good explanation of what's needed would go a long way!
