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train leaves a station at 6 prm,followed by an express train, which leavest 8 pm and travels 20 km/h faster than theoods train. The express train arrives at astation, 1040 km away, 36 min before thegoods train. Assuming that the speeds ofboth the trains remain constant betweenthe two stations, calculate their speeds. |
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Answer» Let the speed of the goods train be x km/hrThen, speed of express train = (x+20) km/hrGoods train leaves a station at 6pm and express train leaves the station at 8pmalso express train reaches its destination 36min before goods train. We known that,Time taken = distance covered /speedTotal distance = 1040 kmTime taken by goods train to cover 1040 km = 1040/x Time taken by express train to cover 1040 km = 1040/(x+20)As per given condition we have,1040/x = 1040/(x+20) + 2(36/60) 1040/x-1040/(x+20) = 2(3/5) (1040x+20800-1040x)/(x²+20x) = 13/5 13x² + 260x = 104000 x² + 20x - 8000=0 x² + 100x - 80x - 8000=0 x(x+100) - 80(x+100)=0 (x-80)(x + 100)=0 x = 80 (or) x = -100Here x>0Therefore x = 80 Hence, speed of goods train = 80 km/hrspeed of express train = 100 km/hr |
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