I'm trying to solve this problem

On a certain high-speed railway line, all trains have the same length and all travel at the same constant speed, faster than I walk. Suppose I start walking east from a certain point, crossing an eastbound train and later a westbound train. The distance between the points where the front and back of the eastbound train pass me is 160 units, while the distance between the points where the front and back of the westbound train pass me is 40 units. Given that each of my steps has length 1 unit, what is the length of each train?

The answer choices are A) 64, B) 80, C) 96, D) 100, and E) 120

What I did: I let the distance of the train be \(t\), the rate of the train be \(r\), and assumed the time per step was 1 second. I then made the two equations. \(t = 160(r-1)\) and \(t = 40(r+1)\). Finding \(r\), I got \(\frac{5}{3}\). This gives me an answer of \(\frac{320}{3}\). Can someone explain to me what I did wrong?

Guest Nov 13, 2021