Concept:Convert all speeds to m/s. Use relative speed to find the first train's speed. Then find relative speed with the second train moving opposite and compute time to cross each other.
Explanation:Given: Length of first train =
325 m. Man's speed =
5 km/hr. Time to overtake man =
45 s.
Second train length =
440 m. Second train speed =
20 km/hr.
Step 1: Relative speed of first train with respect to man (same direction) = distance/time =
325/45=65/9 m/s.
Step 2: Convert man's speed to m/s:
5×(5/18)=25/18 m/s.
Step 3: Speed of first train = relative speed + man's speed =
65/9+25/18=(130/18+25/18)=155/18 m/s.
Step 4: Second train speed in m/s:
20×(5/18)=100/18 m/s.
Step 5: When moving in opposite direction, relative speed = sum =
155/18+100/18=255/18=85/6 m/s.
Step 6: Total distance to cross = sum of lengths =
325+440=765 m.
Step 7: Time = distance / relative speed =
765÷(85/6)=765×(6/85)=54 seconds.
Answer:54 seconds. (Option C)