Final answer:
Without additional details such as the force and duration of the push or the exact masses, we cannot determine which skater has the greater speed after the push-off using only the information provided. To answer this, knowledge about the conservation of momentum is necessary, but the specifics are missing in the given question.
Step-by-step explanation:
The question you're asking relates to the conservation of momentum in physics. When skater B, who is lighter, is pushed off by skater A, who is stationary and heavier, the conservation of momentum tells us that the total momentum before and after the push-off must be the same since no external horizontal forces are acting on the system.
In this scenario, if Skater A is stationary and therefore has no initial momentum, after they push Skater B, Skater B will have a certain momentum. The speed of Skater B right after the push-off depends on the force and duration of the push. However, without specific values for these factors or the exact masses of the skaters, it cannot be determined from the given information which skater will have the greater speed after the push-off.
Now, if we're referring to another scenario where both skaters are already moving and one skater catches the other without applying any horizontal forces, we can apply the conservation of momentum to find the combined speed after one skater picks up the other.