Two trains pass each other on parallel lines. Each train is 100 m long

1.	Two trains pass each other on parallel lines. Each train is 100 m long. When they are going in the same direction, the faster one takes 60 seconds to pass the other completely. If they are going in opposite directions, they pass each other completely in 10 seconds. Find the speed of the slower train in km/ hr. (a) 30 km/hr (b) 42 km/hr (c) 48 km/hr (d) 60 km/hr
Answer» (a) 30 km/hr Let the speed of the faster train be x km/hr and that of the slower train be y km/hr. Relative speed when both move in same direction = (x – y) km/hr Relative speed when both move in opposite directions = (x + y) km/hr Total distance travelled = Sum of lengths of both the trains = 200 m Given, \(\frac{200}{(x-y)\times\frac{5}{18}}=60\) and \(\frac{200}{(x+y)\times\frac{5}{18}}=10\) ⇒ \(\frac{3600}{5(x-y)}=60\) and \(\frac{3600}{5(x+y)}=10\) ⇒ x - y = \(\frac{3600}{300}=12\) ....(i) and x + y = \(\frac{3600}{50}=72\) ....(ii) Adding eqn (i) and eqn (ii), we get 2\(x\) = 84 ⇒ \(x\) = 42 km/hr ∴ From (i), y = 30 km/hr.

Two trains pass each other on parallel lines. Each train is 100 m long. When they are going in the same direction, the faster one takes 60 seconds to pass the other completely. If they are going in opposite directions, they pass each other completely in 10 seconds. Find the speed of the slower train in km/ hr. (a) 30 km/hr (b) 42 km/hr (c) 48 km/hr (d) 60 km/hr

Answer»

(a) 30 km/hr

Let the speed of the faster train be x km/hr and that of the slower train be y km/hr.

Relative speed when both move in same direction = (x – y) km/hr

Relative speed when both move in opposite directions = (x + y) km/hr

Total distance travelled = Sum of lengths of both the trains = 200 m

Given, \(\frac{200}{(x-y)\times\frac{5}{18}}=60\) and \(\frac{200}{(x+y)\times\frac{5}{18}}=10\)

⇒ \(\frac{3600}{5(x-y)}=60\) and \(\frac{3600}{5(x+y)}=10\)

⇒ x - y = \(\frac{3600}{300}=12\) ....(i)

and x + y = \(\frac{3600}{50}=72\) ....(ii)

Adding eqn (i) and eqn (ii), we get

2\(x\) = 84 ⇒ \(x\) = 42 km/hr

∴ From (i), y = 30 km/hr.