A and B start from the same point and in the same direction at 7 am to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 12.30 pm ?

Solution(By Examveda Team)

Perimeter of the field
= 2(400 + 300) m
= 1400 m
= 1.4 km
Since A and B move in the same direction, so they will first meet each other when there is a difference of one round i.e., 1.4 km between the two.
Relative speed of A and B = (3 - 2.5) km = 0.5 km/hr
Time take to cover 1.4 km at this speed :
$$\eqalign{ & = \left( {\frac{{1.4}}{{0.5}}} \right){\text{ hr}} \cr & = 2\frac{4}{5}{\text{ hr}} \cr & = 2{\text{ hr 48 min}} \cr} $$
So, they shall first cross each other at 9.48 am
And again 2 hr 48 min after 9.48 am i,e., 12.36 pm
Thus, till 12.30 pm they will cross each other once.