smc

We can make three equations out of the information, and since the distances are the same, we can equate these equations. $$\frac{4t}{5}(x+\frac{1}{2})=xt=(t+\frac{5}{2})(x-\frac{1}{2})$$ where $x$ is the man's rate and $t$ is the time it takes him. Looking at the first two parts of the equations, $$\frac{4t}{5}(x+\frac{1}{2})=xt$$ we note that we can solve for $x$. Solving for $x$, we get $x=2.$ Now we look at the last two parts of the equation: $$xt=(t+\frac{5}{2})(x-\frac{1}{2})$$ we note that we can solve for $t$ and we get $t=\frac{15}{2}.$ We want the find the distance, which is $xt=\boxed{15}.$