Final answer:
The woman on the left will have a final velocity of 15 m/s in the opposite direction of the girl on the right, assuming they have equal masses, due to the conservation of momentum and Newton's third law.
Step-by-step explanation:
When two skaters standing at rest on an ice rink push off of each other, they exert equal and opposite forces on one another due to Newton's third law of motion. This scenario involves the conservation of momentum, which states that the total momentum of an isolated system remains constant if no external forces are acting on it. Assuming no external forces and that the skaters have different masses, they will move away from each other at speeds inversely proportional to their masses. If the final speed of the girl on the right is 15 m/s, then, by conservation of momentum, the woman on the left must have the same magnitude of momentum but in the opposite direction. Given that no information is provided about their masses, we can only deduce that her speed will be 15 m/s in the opposite direction if we assume the skaters have equal mass. Therefore, the correct answer is b) 15 m/s in the opposite direction of the girl on the right.