Three boats with the same mass P travel in line ahead (one after the other) with the same speed v. Two identical loads of mass P1 each are thrown simultaneously from the middle boat to the front and rear boats with the same speed u relative to the boat. What are the speeds of the boats (v1, v2, and v3) after the loads have been thrown across? My attempts: The speed of the masses relative to the ground will be v+u and v-u. Considering only the second boat and applying conservation of momentum, you get: Pv = (P - 2P1)(v2) + P1(v + u) + P1(v - u), and v2 = v. That part is fine. Now considering all the boats in the initial, final, and intermediate stage: 3Pv = (P+P1)v1 + (P+P1)v3 + (P-2P1)v = 2Pv + (P-2P1)(v) + P(v+u) + P1(v-u). Now the expressions for v1 and v3 as given in the solutions section should not contain v1 or v3, and they must contain u. I don't understand how that's possible since if you simplify the rightmost side of the equation, u is eliminated.