Math  What is the length of the train??????
posted by Anonymous on .
I have NO IDEA on how to tackle the following problem. This question has stumped me for like...2 hours now...and I don't know what to do...
If someone could please show me a step by step on solving it, please post!
Problem:

Two people stand back to back next to the rails in a small railway station. As the head of the express train (which does not stop at this station) reaches them, they start to walk in opposite directions 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 speeds and the train's speed was constant, how long was the train?
Answer:

240m

This stumped me, too. It's not an easy problem. Here's what I turned up on google...
"When the tail of the train reaches the first person, both have walked 30m. Now the second person walks another 10m. During that time the tail of the train travels the 70m between the two persons' endpoints. So the train is seven times faster than each person.
When the tail of the train reaches the second person, the head of the train is 7*40m (seven times faster than the second person!) away from the point where the two persons started. The tail is 40m away from this point  in the same direction. So the train is 240m long." 
What the heck....how do you know the train is seven times faster than each person?