Two straight roads cross at right angles at a junction $O$. Take them as the coordinate axes, with $1$ unit $= 1\ \text{km}$. A village well stands at $P(8, 1)$, that is $8\ \text{km}$ east and $1\ \text{km}$ north of $O$, as in the figure. A straight new road is to be built through the well. It will meet the east road at $A$ and the north road at $B$, both on the positive axes, and it can be turned about $P$ to any such position. The council wants the lengths $OA$ and $OB$ of the old roads used by travellers to be as small as possible together. What is the least possible value of $OA + OB$, in kilometres?

Fig. 1: Coordinate axes with origin O, the x-axis labelled east road and the y-axis labelled north road, unit 1 km. The well P(8, 1) is marked. A straight line through P cuts the positive x-axis at A and the positive y-axis at B. The line is drawn in one sample position only.