This problem involves calculating the speed of a train based on its interaction with a moving man and then determining the time it takes to cross another train moving in the opposite direction. We need to use concepts of relative speed.

Calculating Train Speed

First, find the speed of the train (let's call it $V_T$). The train overtakes a man moving in the same direction. The relative speed is the difference between the train's speed and the man's speed.

• Train length, $L_1 = 220$ m.
• Man's speed, $V_M = 10$ km/hr.
• Time to overtake, $t_1 = 44$ seconds.

Convert the man's speed to meters per second (m/s): $V_M = 10 \times \frac{5}{18} = \frac{50}{18}$ m/s.

The relative speed ($V_{rel1}$) when moving in the same direction is $V_T - V_M$. The distance covered is the length of the train ($L_1$). Using the formula: Distance = Speed × Time

$L_1 = (V_T - V_M) \times t_1$

$220 = (V_T - \frac{50}{18}) \times 44$

$V_T - \frac{50}{18} = \frac{220}{44} = 5 \text{ m/s}$

$V_T = 5 + \frac{50}{18} = \frac{90 + 50}{18} = \frac{140}{18} \text{ m/s}$

Calculating Crossing Time

Next, calculate the time the train takes to cross another train moving in the opposite direction. When moving in opposite directions, the relative speed is the sum of their speeds.

• Train 1 length, $L_1 = 220$ m.
• Train 1 speed, $V_T = \frac{140}{18}$ m/s.
• Train 2 length, $L_2 = 315$ m.
• Train 2 speed, $V_2 = 79$ km/hr.

Convert Train 2's speed to m/s:

$V_2 = 79 \times \frac{5}{18} = \frac{395}{18} \text{ m/s}$

The relative speed ($V_{rel2}$) when moving in opposite directions is $V_T + V_2$.

$V_{rel2} = \frac{140}{18} + \frac{395}{18} = \frac{535}{18} \text{ m/s}$

The total distance to cover for crossing is the sum of the lengths of both trains ($L_1 + L_2$).

Total Distance $= L_1 + L_2 = 220 + 315 = 535$ m.

Using the formula: Time = Distance / Speed

Time to cross ($t_2$) $= \frac{L_1 + L_2}{V_{rel2}}$

$t_2 = \frac{535}{\frac{535}{18}} = 18 \text{ seconds}$

Conclusion

The time taken for the first train to completely cross the second train is 18 seconds.