A train of certain length takes time t to pass completely through a station of length x. The same train with same speed takes time 2t to pass completely through another station of length y. What is the time taken by the train to pass completely through a station of length (x+y)?
- A. (2yt+xt)/(y-x)
- B. (yt+xt)/(y-x)
- C. (3yt-xt)/(2y-x)
- D. (2yt-xt)/(y-x) ✓
Correct Answer: D. (2yt-xt)/(y-x)
Explanation
Let L be train length and v be speed. Equations: L+x = vt and L+y = 2vt. Subtracting gives y-x = vt \implies v = \frac{y-x}{t}. Also L = y-2x. The time to cross (x+y) is \frac{L+(x+y)}{v} = \frac{(y-2x)+x+y}{(y-x)/t} = \frac{(2y-x)t}{y-x} = \frac{2yt-xt}{y-x}.
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