A wooden raft, 5-feet long and 4-feet wide, floats in water. When a person steps on the raft, it sinks 1.5 inches deeper into the water. Calculate the person's weight. Density of the water: 62.4 lb/ft.3

Presumably, the raft is thick enough that it isn't covered by water. Also, we assume that it's truly rectangular.

Archimedes principle: The buoyancy (amount of "lift" to float something) is equal to the weight of the water displaced.

all you have to do is find the volume of the water that was displaced by the sinking raft. That's easy. Then

\frac {lb}{ft^3} \,\times\, ft^3 = lb

If you exert a force of 20N to life a box a distance of 1.93m, how much work do you do?

Use Work\, Done = Force\, \times Distance