An intensive math problem (algebra)?

Question

Two people stand back to back next to the rails in a small railway station. As the head of the express train reaches them they both start walking parralel to the tracks. (in oppostie directions). As the tail of the train reaches each of them they both stop, having walked 30 and 40 meters respectively. If they both walked at the same constant rate and the train maintaned its speed, how long was the train?

Answer 1

240 mts

Lets say lenght of train =X
Speed of train = Y

1) A walks 30 meters(opposite direction of train), so train travelled X-30 meters during the time that A walked. Time taken by train (T1) to travel (x-30) mt = dis/speed = (x-30)/y

2) B walks 40 mts (in direction of train). Train travelled X+40 mts. Time taken by train (T2) to travel (x+40) = (x+40) /y

Note that above T1 and T2 are the time that A and B walked.
Now lets get the speed of A & B

3) Speed of A = distance travelled 30 meter / (T1)
= 30 / ((x-30)/y) = 30y/ (x-30)

4) Speed of B = 40 / T2 = 40y / (X+40)

We have one 'known' -- i.e. speed of A = speed of B

So
30Y / (X-30) = 40Y/(X+40)

--simplify the equation and you get X = 240

Answer 2

OK.
At t0 (initial time), both people are at the same spot.
At t1, the tail of the train reaches the person that walked towards the end of the train.
At t2, the tail of the train reaches the other person.

In the time interval defined between t2 - t1, Person B (the one walking in the same direction as the train) has walked 10 meters, and the train has travelled 70 meters.

In the time interval defined between t1 - t0, Person A has walked 30 meters, and the train has travelled l meters, where l = length of the train.

Since we know that the people waked at a constant rate:
t1 - 10 must be 3* (t2-t1), because person B walked 30 meters in the first interval, and 10 in the second.

t2 - t0 = 4*(t2-t1)

During the entire period, the train travelled l + 40 meters (the +40 meters is the distance person B walked from the initial starting point).
v = (l + 40) / (t2 - t0) (total distance over total time)
v = 70 / (t2 - t1) (distance covered between the tail of the train reaching Person A and Person B.)

(l + 40) / (t2 - t0) = 70 / (t2 - t1)
(l + 40) / (4*(t2-t1)) = 70 / (t2 - t1) (substituting t2 - t0 = 4*(t2-t1))
1/4 * (l + 40) / (t2-t1) = 70 / (t2 - t1)
1/4 * (l + 40) = 70
l + 40 = 70 * 4 = 280
l = 240 m (solution!)

Answer 3

(30 + 40) * 2 = 140

The length of the train was 140 metres.

Answer 4

wow david, u got the right answer 2 out of 3 times, just you got the wrong one first...tough luck