Force Equilibrium
Submerged Water Line 

The total weight of the canoe and the paddlers is
W = 120 lb + 630 lb = 750 lb
For equilibrium, the total weight must be balanced by the buoyant force. That is,
W = F_{B}
where the buoyant force is the weight of the liquid displaced by the volume and is given by
F_{B} = ρgV_{displaced}
The submerged waterline is denoted as h and the displaced volume for
each design will be expressed in terms of h as follows:

Displaced Volume of Design Layout A


The displaced volume of layout A is given by
V_{displaced} = 2 (10 + h) h
Applying force equilibrium yields
750 = (1.94) (32.2) (2) (10 + h)h
h^{2} + 10h  6 = 0
Using the Quadratic Equation gives,
h = 0.5678 ft
The submerged height h (0.568 ft) is less than the height of the
canoe (1 ft), hence this canoe will float. 
Displaced Volume of Design Layout B


The displaced volume of layout B is given by
V_{displaced} = 2 (11 + h) h
Applying force equilibrium yields
750 = (1.94) (32.2) (2) (11 + h)h
h^{2} + 11h  6 = 0
h = 0.5208 ft
The submerged height h (0.521 ft) is greater than the height of
the canoe (0.5 ft), hence this canoe will sink.
