A train leaves Agra at 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Agra at 10:30 a.m. At what time do the two trains cross each other?

Given:

Train 1 leaves Agra station at 5 a.m. and reaches Delhi at 9 a.m.

Train 2 leaves Delhi station at 7 a.m and reaches Agra at 10.30 a.m

Formula used:

Speed = Distance/time

If two objects move with the speeds u & v in opposite direction, then

Relative speed = u + v

Calculation:

Train 1 travel time = 4 hours

Train 2 travel time is 3.5 = \(\frac{7}{2}\) hours

We know, speed = Distance/time

Let the distance b/w Agra & Delhi is 28 Km (LCM of 4 & \(\frac{7}{2}\))

so, speed of 1st train = 28/4 = 7 km/h

⇒ speed of 2nd train = 28/3.5 = 8 km/h

Relative speed = Train 1 speed + Train 2 speed

⇒ Relative speed = 7 + 8 =  15 km

Train 1 travels for 2 hours before train 2 starts.

Remaining distance = 28 - 28/2 = 14 km

Time is taken to cross each other

Time = 14/15 hours or 56 minutes.

Total time taken = 2 hours + 56 minutes

∴ They cross each other at 7 : 56 a.m.