A girl of mass 48 kg stands at one end of a boat of mass 152 kg and length 3.5 m…

Step 1. Set up. Let the boat move $x$ backward. Relative to the shore, the girl moves $L - x$ forward.

Step 2. Balance. $m(L - x) = Mx$, so $48\ \text{kg}(3.5\ \text{m} - x) = 152\ \text{kg}\,x$, which gives $168\ \text{kg m} = 200\ \text{kg}\,x$.

Step 3. Solve. $x = 0.84\ \text{m}$, and the girl moves $3.5\ \text{m} - 0.84\ \text{m} = 2.66\ \text{m}$.