Just for fun, I tired to reason out how far Schlemihl walked that first day, with the following assumptions:
Each stripe is 24 inches long, and separated from the next stripe by 24 inches
The paint brush holds enough paint to paint 1 stripe
There are 1311 stripes per block (1 block = 1 mile, with 36 foot streets separating the blocks that are unpainted)

Where T = trip number, S = stripe length, I = interval between stripes
That makes each trip = T*(S*2)+I(2(T-1))
or Trip 1 = 48"
Trip 2 = 144"
T3 = 240" etc.

total trip = T1+T2+T3...

adding in the width of the streets crossed between blocks, Schlemihl walked an amazing 11,772.18 MILES to paint 3933 stripes on 3 miles of road. At a speed of no less than 1471.5 MPH! (assuming an 8 hour shift)

Assuming he could carry a bucket that held enough paint to paint 3 miles of stripes, he could paint that 3 miles in about 6 seconds.

On the other hand, his performace at a more human speed of 2.5 MPH, he would only be able to paint about 162 stripes in 8 hours (using the old method), or about 12% of a block, and his performace drops even faster than in the example given. He ends up taking 2.5 years to paint stripes on a 3 mile road.

Thanks for the diversion! :-)