Boat-man problem, velocity of center of mass

[Dansuer]

Homework Statement

A man of mass 84.4 Kg is in the back of a boat of mass 425 kg which is moving without friction on ice with velocity 4.16 m/s. the man moves from the back to the top of the boat with velocity 2.08 m/s traveling for 18.2m. How much distance does the boat travel while the man moves?

Homework Equations

v$$_{cm}$$ = (v$$_{1}$$m$$_{1}$$ + v$$_{2}$$m$$_{2}$$)/(m$$_{1}$$+m$$_{2}$$)

The Attempt at a Solution

The way i try to solve this was that i put V$$_{cm}$$ = 0 because i choose a coordinate system with velocity V$$_{cm}$$. The equation on top gives the velocity of the boat to be 0.41 m/s. Subtract this to the velocity of the boat relative to the ice gives v=3.7 m/s
Now i calculated the distance travelled: 18.2 : 2.08 = x : 3.7 which is 32.37

but it's not the same results as the book gives as a solution. What did i do wrong?

 

[cupid.callin]

why are you taking the frame at velocity of CM. take frame at v=0
then you don't need to find the relative speeds, just use them as given

 

[Dansuer]

You're right i could've done that. But the answer to the problem does not change. And it's not the same as the book. Is the book wrong or i am ?

 

[cupid.callin]

I need to sleep now ... its 3AM here ...

But you can post your answer and i'll tell you your mistake as soon as i wake up.
will that work?

 

[Dansuer]

of course, no hurry

You can find my answer in the point 3 of my first post

thanks