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The speed of car is S km/hr running on the road besides a railway track. If the speed of the train is (S + 144) km/hr and car is D meter distance ahead of the engine of train. The train will pass the car in 21 seconds. If the speed of the car is 60 km/hr and the speed of the train is (S + 110) km/hr. The car is (D – 240) meter distance ahead of the engine of the train and the train will pass the car in 20 seconds. The length of the train is (D + 160) m. Then, what is the value of S?

The speed of car is S km/hr running on the road besides a railway track. If the speed of the train is (S + 144) km/hr and car is D meter distance ahead of the engine of train. The train will pass the car in 21 seconds. If the speed of the car is 60 km/hr and the speed of the train is (S + 110) km/hr. The car is (D – 240) meter distance ahead of the engine of the train and the train will pass the car in 20 seconds. The length of the train is (D + 160) m. Then, what is the value of S? Correct Answer 58

Formula:

Distance = Time × Speed

Calculation:

Case I:

The speed of the Car = S km/hr

The Speed of the train = (S + 144) km/hr

Total Time = 21 seconds

Total Distance = (D + D + 160) = (2D + 160) meters

∴ Relative Speed = (S + 144 – S) km/hr = 144km/hr

⇒ 144 × 5/18 m/s

⇒ 40 m/s

∴ Distance = Speed × Time

⇒ (2D + 160) = 40 × 21

⇒ 2D = 840 – 160

⇒ 2D = 680

⇒ D = 340

Case II:

The speed of car = 60 km/hr

Speed of train = (S + 110) km/hr

∴ Relative Speed = (S + 110 – 60) = (S + 50) km/hr

Total Distance = (D – 240) + (D + 160)

⇒ (2D – 80)

⇒ (680 – 80)

⇒ 600 meters

Time = 20 seconds

Thus, Distance = Speed × Time

600 = (S + 50) × 5/18 × 20

⇒ (S + 50) = 6 × 18

⇒ S + 50 = 108

⇒ S = 108 – 50

⇒ S = 58

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