A faster train overtakes a slower train, both moving in the same direction. The faster train takes 36 seconds to completely pass the slower train. A passenger sitting in the faster train observes that he passes the slower train in 12 seconds. Find the ratio of the length of the faster train to the length of the slower train.
2 : 1
Let the faster and slower train lengths be Lf and Ls, and relative speed be v.
Overtaking (passing the whole slower train): \(36v = Lf+Ls\).
The passenger (a point) sees the slower train pass in 12 seconds: \(12v = Ls\).
So \(Lf+Ls = 3\times Ls \Rightarrow Lf = 2Ls\), giving \(Lf:Ls = 2:1\).
Hence, the ratio of the length of the faster train to the slower train is 2:1.
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