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Question

# From a station, two trains start at a same time. One train moves in West and other to North direction. First train moves 5 km/h faster than the second train. If after 2 hours distance between two trains is 50 kms , find the average speed of each train

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Solution

## 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 train Then (s+5) = the speed of the westbound train : This is a right triangle problem: a^2 + b^2 = c^2 The distance between the trains is the hypotenuse dist = speed * time The time is 2 hrs, so we have a = 2s; northbound train distance b = 2(s+5) = (2s+10); westbound distance c = 50; distance between the two trains : (2s)^2 + (2s+10)^2 = 50^2 4s^2 + 4s^2 + 40s + 100 = 2500 : Arrange as a quadratic equation 4s^2 + 4s^2 + 40s + 100 - 2500 = 0 8s^2 + 40s - 2400 = 0 : Simplify, divide by 8: s^2 + 5s - 300 = 0 : Factors to (s - 15)(s + 20) = 0 : The positive solution is what we want here s = 15 mph is the speed of the northbound train then 5 + 15 = 20 mph is the speed of the westbound train

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