A train 250 m long crosses a man running at a speed…

Solution:

Length of train = 250 m
Speed of man = 7 km/h
Time taken to cross the man = 36 sec

Since the man and train are moving in the same direction:

Relative speed of train and man:

$\frac{250}{36} = \frac{125}{18}$ m/s

Convert the man's speed:

$7 \times \frac{5}{18} = \frac{35}{18}$ m/s

Therefore, speed of train:

$\frac{125}{18} + \frac{35}{18} = \frac{160}{18} = \frac{80}{9}$ m/s

Now, the second train is 415 m long and moves in the opposite direction at 82 km/h.

Speed of second train:

$82 \times \frac{5}{18} = \frac{205}{9}$ m/s

Relative speed:

$\frac{80}{9} + \frac{205}{9} = \frac{285}{9} = \frac{95}{3}$ m/s

Total distance to be covered:

250 + 415 = 665 m

Time taken:

$\frac{665}{95/3} = \frac{665 \times 3}{95} = 21$ seconds

Correct Answer: 2. 21 seconds