Chapter 2.5, Problem 118E

Business: minimizing distance. A road is to be built between two cities $C_1$ and $C_2$, which are on opposite sides of a river of uniform width r. $C_1$ is a units from the river, and $C_2$ is b units from the river, with $a\le b$. A bridge will carry the traffic across the river. Where the bridge should be located in order to minimize the total distance between the cities? Give a general solution using the constants a, b, p, and r as shown in the figure.

$x=\frac{bp}{a+b}$