The (x-t) graph for the motion of the drunkard is shown in the fig. It is clear from the graph that he takes 37 seconds to fall in the pit.
The distance of the pit from the start = 13 m.
The time taken to move first 5 m = 5 sec.
5 steps (i.e., 5m) forward and 3 steps (i.e.,3 m) backward means that net distance covered = 5 - 3 = 2 m and time taken during the process
= 5 + 3 = 8 sec.
Time taken in moving 8 m = 8 x 8/2 = 32 second.
The distance of the pit form the drunkard after covering a net distance of 8 m = 13 - 8 = 5 m.
Now, in next 5 steps forward, the drunkard will fall into the pit, for which he will take 5 sec. more i.e., total time taken to fall in the pit.
= 32 + 5 = 37 sec.