Two trains, 135 km/hr and 32.5 m/s, cross each other in 20 seconds when moving in opposite directions. How long do they take to cross if they move in the same direction?

Step 1: Convert the speed of the first train from kilometers per hour to meters per second. The speed of the first train is S_1 = 135 km/hr. To convert km/hr to m/s, we multiply by (5)/(18). S_1 = 135 × (5)/(18) m/s = (675)/(18) m/s = 37.5 m/s The speed of the second train is S_2 = 32.5 m/s. Comparing the speeds, S_1 = 37.5 m/s is the faster train. Step 2: Calculate the relative speed when the trains travel in opposite directions. When two trains travel in opposite directions, their relative speed is the sum of their individual speeds. S_rel, opp = S_1 + S_2 = 37.5 m/s + 32.5 m/s = 70 m/s Step 3: Calculate the total length of the two trains. When two trains cross each other, the total distance covered is the sum of their lengths (L_1 + L_2). Given that they take 20 seconds to cross each other in opposite directions: L_1 + L_2 = S_rel, opp × T_opp L_1 + L_2 = 70 m/s × 20 s = 1400 m Step 4: Calculate the relative speed when the trains travel in the same direction. When the faster train crosses the slower train from behind (traveling in the same direction), their relative speed is the difference between their speeds. S_rel, same = S_faster - S_slower = S_1 - S_2 = 37.5 m/s - 32.5 m/s = 5 m/s Step 5: Calculate the time taken for the faster train to completely cross the other train in the same direction. The distance to be covered for one train to completely cross the other is still the sum of their lengths, which is L_1 + L_2 = 1400 m. T_same = (L_1 + L_2)/(S_rel, same) T_same = 1400 m5 m/s = 280 s The time taken by the faster train to completely cross the other train from behind while traveling in the same direction is 280 seconds. That's 2 down. 3 left today — send the next one.