1. **Problem statement:** Two people are pulling on either end of a rope with forces of 20 N to the left and 30 N to the right. We need to find the resultant force on the rope. 2. **Formula and rules:** The resultant force when two forces act in opposite directions is the difference between their magnitudes, and the direction is that of the larger force. $$F_{resultant} = |F_2 - F_1|$$ 3. **Calculation:** $$F_{resultant} = |30 - 20| = 10$$ 4. **Direction:** Since 30 N is greater and acts to the right, the resultant force is 10 N to the right. 5. **Explanation:** When two forces pull in opposite directions, the rope experiences a net force equal to the difference of the two forces, pointing toward the stronger pull. **Final answer:** The resultant force on the rope is 10 N to the right.