Solving Speed of Objects Problem

[yankees26an]

Homework Statement

A bomb that is originally at rest blows apart into three pieces of equal mass. Two of the
pieces have velocities (12i + 24j) m/s and (30i - 24j) m/s. What is the speed of the third
piece?

Homework Equations

m1v1 + m2v2 + m3v3 = 3mv4 (assuming m is the same)

The Attempt at a Solution

Not really sure where to begin. I can find the speed of the 2 objects by finding the k direction, but that's it.

 

[Doc Al]

Hint: What's the total momentum of all three pieces?