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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?





Solution

Train Collision Problem

Navjivan Express leaves Ahmedabad at 6:30 am traveling at 50 km/h towards Baroda (100 km away).
At 7:00 am, Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad at 40 km/h.
At 7:30 am, Mr. Shah realizes both trains are on the same track heading toward each other.

Step 1: Navjivan distance by 7:30 am = 50 km/h × 1 h = 50 km
Step 2: Howrah distance by 7:30 am = 40 km/h × 0.5 h = 20 km
Step 3: Distance between trains at 7:30 am = 100 − (50 + 20) = 30 km
Step 4: Relative speed = 50 + 40 = 90 km/h
Step 5: Time until collision = 30 km / 90 km/h = 1/3 hour = 20 minutes

Time to avert collision: 20 minutes



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