Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively.
If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was?  Answers
A) 140m  B) 240m  C) 340m  D) 440m  E) 540m
Let d be the length of the train, and   let t1 be the time it took for the tail of the train to reach   the first person, and   let t2 be the time it took for the tail of the train to reach   the second person.   By time t1, the head of the train is d-30 meters beyond the point where it passed the two people.   By time t2, the head was d+40 meters beyond where it passed the two people. The ratio of these distances,   d-30 : d+40   is equal to the ratio of t1:t2, because the train is moving at a constant speed.   Since both people walk at the same constant rate, this ratio is 3:4.   d-30 : d+40 = 3:4   The product of the means equals the product of the extremes, so   3(d+40) = 4(d-30)   3d + 120 = 4d - 120   240 = d   Answer 240m
<result>B</result>
Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively.
If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was?