Solving Speed of Objects Problem

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