Question 33 Two trains travelling at speeds of 100 km/h and 170 km/h respectively take 3...
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Two trains travelling at speeds of 100 km/h and 170 km/h respectively take 3 seconds to cross each other. If the length of the slower moving train is 1.5 times the length of the faster moving train, then what is the length of the faster moving train?
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Relative speed is 100 + 170 = 270 km/h = 75 m/s. In 3 seconds, total distance covered is 75 * 3 = 225 m. Sum of lengths is L + 1.5L = 2.5L = 225 m, giving L = 90 m.
Step-by-step Derivation:
Step 1: Relative speed of two trains moving in opposite directions = 100 + 170 = 270 km/h.
Step 2: Convert to m/s: 270 * (5/18) = 75 m/s.
Step 3: Distance covered in 3 seconds = 75 * 3 = 225 m.
Step 4: Sum of lengths = L_fast + L_slow = L + 1.5L = 2.5L.
Step 5: 2.5L = 225 => L = 225 / 2.5 = 90 m.