A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5

Question

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is $1	ext{ m}$ long and requires $1	ext{ s}$. How long will he take to fall into a pit $13	ext{ m}$ away from the start?

Professor PC Thomas Classes · Answer

In each cycle of 8 steps (8 seconds), he moves $5 - 3 = 2	ext{ m}$ forward. To reach $8	ext{ m}$, he completes 4 cycles, taking $4 	imes 8 = 32	ext{ s}$. From the $8	ext{ m}$ mark, he takes 5 steps forward in the next 5 seconds to reach the $13	ext{ m}$ mark and falls into the pit. Total time $= 32 + 5 = 37	ext{ s}$.