Calculating Distance Moved by Boat with a Boy Aboard

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To calculate the distance moved by the boat when the boy moves from the stern to the bow, the principle of conservation of momentum is applied, keeping the center of mass at rest. The equation M_boat * ΔX_boat + m_boy * ΔX_boy = 0 is used, where M is the mass of the boat and m is the mass of the boy. By establishing a reference frame at the bow of the boat, the displacement of the boy can be expressed in terms of the boat's movement. The boy's displacement is calculated as ΔX_boy = x - l, where l is the length of the boat. This approach allows for determining the exact distance the boat moves as the boy shifts positions.
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The mass of a boat is M=80kg, the mass of a boy is m=36kg. The boy moves from the stern to the bows of the boat. What distance does the boat move, if its length is 2.8m? At such low speeds the water resistance may be neglected. Hint: Center of mass remains at rest.

Please help becuase I am stumped... :confused:
 
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M_{boat} \Delta {X_{boat}} + m_{boy}\Delta {X_{boy}} =0

Coose ur reference frame let it be at the bow of the boat
Now dboy=dboy/boat+dboat

Let x be the displacement of boat then (Delta)Xboat = x
then
dboy = x-l

Where l is the length
 

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