Two trains of length 100 m and 80 m respectively run on parallel lines of rails. When running in the same direction the trains pass each other in 18 s, but when they are running in opposite directions with the same speeds as earlier, they pass each other

Two trains of length 100 m and 80 m respectively run on parallel lines of rails. When running in the same direction the trains pass each other in 18 s, but when they are running in opposite directions with the same speeds as earlier, they pass each other in 9 s. Determine the speed of the faster train.
1). 5 m/s
2). 10 m/s
3). 15 m/s
4). 20 m/s

Let the speeds of both trains be ‘x’ and ‘y’.

When running in same directions, their relative velocity = x – y

Total distance to cross each other = 100 + 80 = 180

speed = distance/time = x – y = 180/18 = 10             ? they take 18 s to cross here

⇒ x – y = 10    ------Equation (1)

When running in opposite direction, relative velocity = x + y

speed = distance/time = x + y = 180/9 = 20   ? they take 9 s to cross here

⇒ x + y = 20    ------Equation (2)

Adding (1) and (2) = 2x = 30 ⇒ x = 15 m/s

⇒ Equation (1) ⇒ 15 – y = 10 ⇒ y = 15 – 10 = 5 m/s

∴ x = 15 m/s and y = 5 m/s

∴ Speed of faster train = x = 15 m/s

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