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Two trains leave a railway stationthe same time. The first train travtowards west and the second train twards north. The first train travelskm/hr faster than the second trainafter two hours they are 50 km. apafind the average speed of each trair |
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Answer» Two trains leave the railway station at the same time.The first travels due west and second train due north.The speed of the first train is 5 km faster than the second train.After two hours they are 50 km apart. Find the average speed of the trains:Let s = the speed of the northbound trainThen(s+5) = the speed of the westbound train:This is a right triangle problem: a^2 + b^2 = c^2The distance between the trains is the hypotenusedist = speed * timeThe time is 2 hrs, so we havea = 2s; northbound train distanceb = 2(s+5) = (2s+10); westbound distancec = 50; distance between the two trains:(2s)^2 + (2s+10)^2 = 50^24s^2 + 4s^2 + 40s + 100 = 2500:Arrange as a quadratic equation4s^2 + 4s^2 + 40s + 100 - 2500 = 08s^2 + 40s - 2400 = 0 |
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