If a cell that is 80% water is placed in a solution that is 40% water, which way
will the net movement of water go?

For healthy flow of water in and out of the cell, the cell should be in an isotonic environment, where the amount of solute (nutrients & particles dissolved in water, such as NaCl) dissolved in the water is equal in and out of the cell so the net water moving in and out of the cell is the same and it will not shrink or swell.
If the cell is placed in a saturated solution that is only 40% water, the solution is a  hypertonic solution meaning that the solute concentration is higher outside the cell than inside the cell. 
Because water molecules can passively dissfuse across the cell membrane, the water molecules will diffuse across the membrane so that the levels outside and inside the cell are equal- causing water to flow out of the cell. The cell will shrink and not perform at its peak.