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284. A train travels a distance of 300 km at a constant speed. If the speed of the train is increased bykm an hour, the journey would have taken 2 hours less. Find the original speed of the trainE 11 |
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Answer» Let speed be 's ', time be 't ' and distance be 'd 't, t = d / s t = 300 / s,d = (s + 5)(t -2)=> d = (s+5)(300/s-2) {t=300/s}=> 300s = (s+5)s(300/s-2) [multiplyning both sides with s]we get = > 300s = (s+5)(300 - 2s)=> 300s = 300s - 2s2+1500 - 10s=>300s =300s-2s2+ 1500 - 10s=> 0 = -2s2+1500 - 10s=> 0 = 2s2+10s - 1500 [multiplying both sides -1 ]=> 0 = 2s2+60s - 50s - 1500=> 0 = 2s(s + 30) -50(s + 30)=> 0 = (2s - 50)(s + 30)=> s = 25, -30 Since, speed cannot be negative, we take speed 25Km/h. |
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