Velocity and distance ratio problem

[JyN]

How do u show, without using calculus, that if something initially has 3 times the velocity of another object, how much farther it will travel than the other?

the exact question is: 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 init with the block reassembled. the reassembled block is set on a rough-surfaced tabble, and the fuse is lit. When the firecracker explodes, the two blocks separeate and slide apart. What is the ratio of distances each block travels?

I have found that the velocity of the small block will be 3 times that of the other using momentum equations p=mv

So how do i show that the small block will travel 9 times (right?) farther than the other?

 

[JyN]

I think i got it actually. I showed that the 2 blocks will accelerate at the same (negative) rate using Newtons 2nd law, and friction (i ignored the initial acceleration from the impulse of the firecracker). then used the equation (Vf)^2 = (Vi)^2 + 2a(Xf-Xi) and did some subs after having determined the velocity of the smaller block will be three times that of the larger one. And ended with with a ratio of 1/9, large block/small block, after doing some canceling. Does it sound like i did this right? how else would other ppl do it?