I'm curious about how long we've described distances as "walking" and if it's been used over a long period, what distance did it refer to over time?
The Online Etymological Dictionary, while including walking sickness, [from 1846], walking wounded [from 1917], walking bass and walking stick does not cover this compound.
A Google 2-gram shows few examples before 1850, including false positives such as ' ... was induced to jump off before reaching station by an accompanying passenger, to economize walking distance' (ie to minimise the distance it was necessary to walk).