Question

A drunken person is two steps away from a manhole. Suddenly he begins to walk towards the manhole. He walks two steps forward and one step backward in one second. Find
A) the time taken after which the person falls into the manhole.
B) distance travelled before he fell into the manhole.

Answer 1

Let us first find the distance travelled by the drunken man in one second. After that, we need to find out the total time taken by him to travel the distance between manhole and his initial position. After that, we need to find the distance travelled by him. It is given that he travels three steps for one second. So, we need to find them accordingly.

Complete answer:
Let us write down the given terms,
The drunken man travels three steps in one second. Two steps are in the forward direction and one step is in the opposite direction, that is backwards. The distance between the drunken man and the manhole is ten steps in total.
Let us find the time taken by the drunken man before he falls into the manhole.
In one second, the distance travelled by the drunken man is two steps forward and one step backward, it means he moves one step forward in whole.
Therefore, for each second, he moves one step forward. As the manhole is ten steps far, and he moves two steps forward each second, we need to calculate for 8 steps first.
Therefore, after travelling for eight seconds, in the ninth second, he falls into the manhole after nine seconds.
Therefore, the dunked person falls into the manhole after nine seconds.
Next, we need to find the distance travelled by the drunken man before he falls into the manhole.
Every second, he travels a total of three steps, two steps in the forward direction and one step backward. So, for eight seconds, he travels a distance of $s = 8\times 3 = 24m$. Now, after eight seconds, he falls into the manhole when he travels two more steps. So, these two steps also come under the distance traveled.
So, total distance is $s = 24+2 = 26m$.
Hence, the time taken is nine seconds and the distance traveled is 26m.

Note:
In the above question, the difference between distance and displacement plays a very important role. If we were asked to find the total displacement by the drunken man, it would only be 10 steps because displacement is the shortest distance between two points. So, we need to be careful in such cases.