Okay, really tough for me atleast.
Answers are 1.15 m/s and 0.346 m/s
edit: title = tough*
Conservation of momentum. Or that the center of mass of the girl-plank system must remain stationary since there is no outside force on the system.
Be careful with speeds. If the plank's speed, relative to the ice is v, then the girl's speed relative to the ice is (1.5+ v) m/s (of course, the plank moves opposite to the girl so v will be negative). The girl's momentum, then, is
45(1.5+ v) kgm/s and the plank's is 150 v kgm/s. By conservation of momentum, 45(1.5+ v)+ 150v= 0.
Got it... Thanks!
Separate names with a comma.