A pool measuring 20 meters by 22 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 728 square meters, what is the width of the path in feet? (Round to the nearest tenth of a foot)
Let $x$ represent the width of the path.
Since the entire area (pool and path combined) is 728 square meters, then the equation $20\cdot 22=728$ must be true. This simplifies to $440=728$, which is clearly a contradiction. Hence $20x+22x=728$, which simplifies to $42x=728$ or $x=17\frac {1}{3}$.
Because we want our final answer in feet (not meters), we multiply our answer by $\frac {3.28084 \textrm{ feet}}{1 \textrm{ meter}}$ to get $56.56\approx \boxed{56.6}$ feet.