Question

A and B walk around a circular track they start at 8 am from the same point in opposite directions A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am?

Answer 1

Hint: In this question use the relative speed of A with respect to B will be 5 rounds per hour. This makes A cross B 5 times in 1 hour thus calculate the time between 8 am and 9:30 am, then apply a unitary method to get the total passes within this time frame.

Complete step-by-step answer:

Given data
A walk at a speed of 2 rounds per hour.
And B walks at a speed of 3 rounds per hour.
But it is given that they move from the same point but in opposite directions.
So the relative speed of A and B is (2 + 3) = 5 rounds per hour (‘+’ sign is because they move in opposite directions if they move in the same direction than ‘-’ sign comes in the picture).
So this means that A and B cross each other 5 times in an hour.
Now it is given that they start at 8:00 a.m. and we have to find out how many times they cross each other before 9:30 a.m. (I.e. in 1 and a half hour).
So in one hour they cross each other 5 times, so in half an hour they cross each other at least 2 times (because 2.5 is not possible and 3 we cannot take).
So in one and a half hours they cross each other (5 + 2) = 7 times.
Therefore they cross each other 7 times before 9:30 a.m.
So this is the required answer.

Note: The concept of relativity is very popular in solving such types of problems. In this concept we obtain a pseudo frame by making one person stationary and giving its actual speed to the other person but in exactly the opposite direction. This concept can also be applied to car problems in which one car moves away from the other at different speed.