Question
Train P starts from Lucknow to Dehradun at 11:55 am with
an average speed of 22.5 m/s. Train Q starts from Dehradun to Lucknow at 1:35 pm with an average speed of 17.5 m/s. At what time the two trains will meet each other if the distance between Lucknow and Dehradun is 615 Km.ÂSolution
Given: Distance between Lucknow and Dehradun = 615 km Speed of Train P = 22.5 m/s = 22.5 × 3.6 = 81 km/h Speed of Train Q = 17.5 m/s = 17.5 × 3.6 = 63 km/h Train P starts at 11:55 AM Train Q starts at 1:35 PM Step 1: Time gap between starts = 1 hr 40 min = 1 + 40/60 = 5/3 hr Step 2: Distance covered by Train P before Train Q starts = 81 × 5/3 = 135 km Remaining distance = 615 - 135 = 480 km Step 3: Relative speed = 81 + 63 = 144 km/h Time taken to meet = 480 / 144 = 10/3 hr = 3 hr 20 min Step 4: Meeting time = 1:35 PM + 3 hr 20 min = 4:55 PM Final Answer: The two trains meet at 4:55 PM.
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