A train of certain length takes time t to pass completely through a station of length x. The same train with the 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)?
(2yt - xt) / (y - x)
Let the length of the train be L and its speed be v.
We know the time taken to pass a station of length x is t, and the time taken to pass a station of length y is 2t.
The time taken to pass a station is given by the formula:
Time = (Train Length + Station Length) / Speed
For the first station (length x), we have:
t = (L + x) / v
For the second station (length y), we have:
2t = (L + y) / v
Now, we solve for L (length of the train) and v (speed of the train):
From the first equation, we get:
L + x = v * t (1)
From the second equation, we get:
L + y = v * 2t (2)
Subtract equation (1) from equation (2) to eliminate L
(L + y) - (L + x) = v * 2t - v * t
y - x = v * t
Thus, we can express the speed as:
v = (y - x) / t
Now, we need to find the time T taken by the train to pass completely through a station of length (x + y). Using the formula for time again:
T = (L + x + y) / v
Substitute the expression for L from equation (1) into this:
T = ((v * t - x) + x + y) / v
Simplify this expression:
T = (v * t + y) / v
Substitute the value of v:
T = ((y - x) / t * t + y) / ((y - x) / t)
Finally, simplify the expression:
T = (2yt - xt) / (y - x)
This matches option 4. Therefore, the correct answer is:
(2yt - xt) / (y - x)
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