momentum conservation law: Head on elastic collision

Hi guys,

I've been thinking on a problem for a while which really bothers me. I've been trying to mathematically solve the following problem:

A train approaches the station at a velocity of V=50 m/s. Then a tennis ball is thrown with a velocity U=30 m/s, against the approaching train. Assume that the collision is absolutely elastic.
If the train's velocity after the collision is V=50 m/s, then what is the speed of the ball with respect to the train station?

So, here is my approach to the problem:

From the momentum conservation law and the fact that the train will have the same momentum after the collision, we can write:

M_trainV - m_ballU = M_trainV + m_ballU_final

so it turns out that the velocity of the ball will be:

U_final = - U = -30 m/s

Which is incorrect. The correct answer should be:

U_final = 2V+U = 130 m/s

Can someone provide a rigorous derivation of the later equation?

Your help will be highly appreciated!