A 225 m long train is running at a speed of 30 km/hr. How much time does it take to cross a man running at 3 km/hr in the same direction?a)40 secondsb)30 secondsc)25 secondsd)15 secondsCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Problem Statement:
A train of length 225 m is running at a speed of 30 km/hr. It has to cross a man running in the same direction at 3 km/hr. We need to find out how much time it will take for the train to cross the man.

Solution:
Given, length of the train = 225 m
Speed of the train = 30 km/hr = 30 x 5/18 m/s = 25/3 m/s
Speed of the man = 3 km/hr = 3 x 5/18 m/s = 5/6 m/s

When the train is crossing a man running in the same direction, the effective speed of the train with respect to the man will be the difference of their speeds.
Effective speed of train = (Speed of train - Speed of man) = (25/3 - 5/6) m/s = 65/6 m/s

Now, we can use the formula to find out the time taken by the train to cross the man.
Time taken = Distance / Speed
Distance = Length of the train = 225 m
Speed = Effective speed of train = 65/6 m/s

Time taken = 225 / (65/6) = 30 seconds

Therefore, the time taken by the train to cross the man running at a speed of 3 km/hr in the same direction is 30 seconds. Hence, option B is the correct answer.

Answer

Sol:- Relative speed between man and train is 30-3=27km/hr

speed = 27*(5/18)=15/2 m/s

time taken by the train to cross the man t = 225/(15/2)
= 30 sec.
so, Option B is correct

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