SOLUTION: Two railroad tracks intersect at right angles at station O. At 10AM the train A, moving west with constant speed of 50 km/h, leaves the station O. One hour later train B, moving so

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Question 900494: Two railroad tracks intersect at right angles at station O. At 10AM the train A, moving west with constant speed of 50 km/h, leaves the station O. One hour later train B, moving south with the constant speed of 60 km/h, passes through the station O. Find minimum distance between these trains
Answer by Alan3354(69443) About Me  (Show Source):
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Two railroad tracks intersect at right angles at station O. At 10AM the train A, moving west with constant speed of 50 km/h, leaves the station O. One hour later train B, moving south with the constant speed of 60 km/h, passes through the station O. Find minimum distance between these trains
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t = 0 at 1000
s+=+sqrt%28%2850t%29%5E2+%2B+%2860+-+60t%29%5E2%29
s+=+sqrt%282500t%5E2+%2B+3600t%5E2+-+7200t+%2B+3600%29
s+=+sqrt%286100t%5E2+-+7200t+%2B+3600%29
ds/dt = (1/2)(12200t - 7200)/sqrt(6100t^2 - 7200t + 3600)}}} = 0
12200t = 7200
t = 0.59016 hours past 1000
t =~ 10:35:24.6
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At that time,
s =~ 38.411 km