Calculate speed of first train

Since the train crosses a man standing on a platform, it covers its own length. Speed $v_1$ is:

$v_1 = \frac{200}{10} = 20 \text{ m/s}$

Convert speed of second train to m/s

Convert $v_2 = 60 \text{ km/h}$ to m/s by multiplying with $\frac{5}{18}$:

$v_2 = 60 \times \frac{5}{18} = \frac{50}{3} \text{ m/s}$

Calculate relative speed and total distance

Since trains move in opposite directions, relative speed is the sum of speeds. Total distance is the sum of lengths.

$v_{rel} = 20 + \frac{50}{3} = \frac{110}{3} \text{ m/s}, \quad D_{total} = 200 + 350 = 550 \text{ m}$

Calculate time taken

Apply the time formula:

$t = \frac{550}{\frac{110}{3}} = 550 \times \frac{3}{110} = 15 \text{ s}$