Painter puzzle - estimation

Question

This problem is based on a puzzle by Joel Spolsky from 2001.

A guy \"gets a job as a street painter, painting the dotted lines down the middle of the road.\"

Answer 1

considering four assumptions :-

painting speed = infinity

walking speed = x

he can paint only infinitly small in one brush stroke.

he leaves his can at starting point.



The distance he walks for painting dy road at y distance = 2y

Total distance he walks = intgeration of 2y*dy = y^2 = y^2

Total time he can paint y distance = y^2/x

Time taken to paint 300 yards = 1 day

(300)^2/x = 1

x = 90000 yards/day

Total time he can paint distance y = y^2/90000


(y/300)^2 = 2      after second day

y = 300*2^(1/2) = 424

Day 1 = 300
Day 2 = 424-300 = 124
Day 3 = 300*3^(1/2)-424 = 520 - 424 = 96

Ans : 300/124/96  assuming the first day its 300