2. Town A is 16 miles from a straight river and Town B is 7 miles from the same river. The distance from Town A to Town B is 15 miles. A pumping station is to be built along the river to supply water to both towns. Where should the pumping station be built so that the sum of the distances from the pumping station to the towns is a minimum? Include a diagram and answer to the nearest hundredth. Assume Town A is west of Town B.
The point we must find is at point P on the diagram.
The distance along the shore between the towns is 12 miles. Because
We must find the length of x by using Pythagoras.
The sum of the distances is given by:
This is what must be minimized. Can you continue?