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Two cars start from the same point and move in opposite directions at speeds of 60 km/hr and 40 km/hr. After how much time will they be 450 km apart?
4.5 hours
5 hours
4 hours
3.5 hours
5 hours
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. In this case, the relative speed is 60 + 40 = 100 km/hr, and applying the formula Time = Distance / Speed (450 / 100) results in 4.5 hours.
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. In this case, the relative speed is 60 + 40 = 100 km/hr, and applying the formula Time = Distance / Speed (450 / 100) results in 4.5 hours.
This problem relates to the concept of Relative Motion, a fundamental principle in classical mechanics defined by Sir Isaac Newton in his Principia Mathematica, which remains the cornerstone for physics problems in Indian railway recruitment exams.
Relative speed in opposite directions is calculated by adding the individual speeds of the objects.
The basic formula for time is Time = Total Distance / Relative Speed.
Railway recruitment board exams (RRB) frequently feature time-speed-distance problems with a weightage of 10-15% in the Mathematics section of CBT-1.
Opposite direction scenario: Relative speed = Speed1 + Speed2.
Same direction scenario: Relative speed = |Speed1 - Speed2|.
Option B (5 hours) would result in a distance of 500 km.
Option C (4 hours) would result in a distance of 400 km.
Option D (3.5 hours) would result in a distance of 350 km.
A is correct тАФ The relative speed is 100 km/hr and 450 km divided by 100 km/hr equals 4.5 hours.
Always verify the direction of motion before calculating relative speed; confusing additive relative speed (opposite) with subtractive relative speed (same direction) is the most common error in RRB mathematics sections.
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