Question 147
Two villages, $A$ and $B$, lie on opposite sides of a straight river in the positions shown. There will be a market in village $B$, and residents of village $A$ wish to attend. The people of village $A$ would like to build a bridge across and perpendicular to the river so that the total route walked by residents of $A$ to the bridge, across the bridge, and onward to $B$ is as short as possible. How can they find the exact location of the bridge, and how long will the route be?