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Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?

Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains? Correct Answer 15 min

Given: 

Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50km/h towards Baroda 

At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 km/h

At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track

The distance between Ahmedabad to Baroda is 100 km.

Concept: 

Time = Distance/Speed

Calculation: 

At 7.30 AM, Distance travel by Navijan express is 

⇒ 50 × 1

⇒ 50 km

At 7.30 AM, Distance travel by Howrah-Ahmedabad Express is 

⇒ 40 × 1/2

⇒ 20 km

Now, Distance left between the both train is 

⇒ 100 - 50 - 20

⇒ 30 km

Both train travel in opposite direction, then relative speed of the trains is 

⇒ 50 + 40

⇒ 90 km/h

Time taken to cover this distance by both train is 

⇒ 30/90

⇒ 1/3 hour = 20 min

So, He have to time less than 20 min to avert the head on collision between two trains.

∴ 15 min

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