A train 75 metres long overtook a person (going in the same direction) who was walking at the rate of 6 km an hour, and passed him in \(7\frac{1}{2}\) seconds. Subsequently it overtook a second person (going in the same direction), and passed him in \(6\frac{3}{4}\) seconds. At what rate was the second person travelling?
Solution
Correct Answer: Option A
When the train passes the 1st person,
Distance covered by the train = 0.075 km
Speed (Relative) = x – 6
(where x is the the assumed speed of the train)
Time = 7.5/3600 hrs
Speed = Distance/Time
∴ x – 6 = \(\frac{{0.075}}{{\frac{{7.5}}{{3600}}}}\)
∴ x = 42 km/hr
Thus the speed of the train is 42 km/hr
Case 2: When the train passes the 2nd person
Distance = 0.075 km
Time = 6.75/3600 hrs
Speed = 42 – y
(Where y is assumed to be the speed of the 2nd person)
Speed = Distance/Time
∴ 42 – y = 0.075/(6.75/3600)
∴ y = 2km/hr
Thus the 2nd person was walking with the speed of 2km/hr
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