What Are the Velocities of the Broken Parts in a Plane Explosion?

[kalupahana]

Homework Statement

A plane of a mass 5000 kg moving horizontally in 150 m/s break into two parts 2000 kg and 3000 kg because of a internal explosion. If the bigger part be thrown away with a 400 m/s relative to other part to opposite direction of previous moved direction before explosion, find the velocity of each part. [Ignore the air resistance]

Homework Equations

Conservation of momentum
E=mv²/2

The Attempt at a Solution

I tried this, but I failed to do this one.

I don't know this is right or wrong
According to conservation of momentum

5000 x 150 - 3000u = 5000 x (400 - 150) - 400 x 3000
3(400 - u) = 50
1200 -3u = 50
1150 = 3u
u = 383.6

color black = Initial momentum of whole plane,
color blue = Initial momentum of 3000 kg part
color lime = final momentum of 3000 kg part
color red = final velocity of whole plane

The part in red or final velocity of whole plane. Is it right to take like that. I multiplied mass by the difference of initial velocity of plane and final velocity of 3000 kg part.

Please help me to do this

 

[kalupahana]

According to the answer script, the two velocities are 310 m/s and 90 m/s. My all tries are went wrong. I could not reach to this.