Machine A and Machine B work at constant rates. How many hours does it take Machine A alone to complete a certain task?

✓ Correct Answer: Option C

Let R_A and R_B be the rates of Machine A and B respectively. Let T_A be the time for A alone. (1) R_A + R_B = 1/12 (work per hour). Insufficient. (2) R_A = 2R_B. Insufficient. Together: Substitute R_B = R_A/2 into (1): R_A + R_A/2 = 1/12. 1.5R_A = 1/12. R_A = (1/12) / 1.5 = 1/18. So, T_A = 1/R_A = 18 hours. Sufficient.