What Is the Ratio of Distances Each Block Travels After a Firecracker Explosion?

[pb23me]

Homework Statement

A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ration of distances each block travels?

Homework Equations

4mv=3mv-mv
4mv=0 so 3v=v

The Attempt at a Solution

I see that one velocity is one third of the other but I am not sure what answer to give as to how far each block travels?

 

[Doc Al]

You don't need to know how far, just the ratio of their distances.

Hint: If you run twice as fast as I do (and we start at the same time and go in opposite directions), what's the ratio of our distances from the starting point at any time? (Make up some numbers and see how it works.)

 

[pb23me]

ok it seems like it would just be 1/3

 

[Doc Al]

That's it.