A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m x 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 p.m.?
- ANot even once
- BOnceCorrect
- CTwice
- DThrice
Explanation
The perimeter of the rectangular field is 2 times (400 + 300) = 1400 meters = 1.4 kilometres.
Since A and B walk in the same direction, the relative speed is 3 - 2.5 = 0.5 km/hr.
For A to overtake B (cross at the starting point again), A must gain one full perimeter over B. Time required = 1.4 km / 0.5 km/hr = 2.8 hours.
Total walking time from 7 a.m. to 12:30 p.m. is 5.5 hours.
First crossing occurs at 2.8 hours. Second crossing would occur at 5.6 hours, which exceeds the total walking time of 5.5 hours.
Therefore, they cross each other exactly once.
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