Machine A can complete a batch of wafer processing in 8 hours. Machine B can do the same job in 12 hours. If both machines are turned on simultaneously, but Machine A is shut down 2 hours before the processing is complete, how many total hours did the processing take?
Explanation:
Let the total work be LCM(8, 12) = 24 units.
Efficiency of A = 24 / 8 = 3 units/hour.
Efficiency of B = 24 / 12 = 2 units/hour.
Let the total time taken to complete the job be x hours.
Machine A worked for (x - 2) hours, and Machine B worked for the full x hours.
Equation: 3(x - 2) + 2(x) = 24 implies 3x - 6 + 2x = 24 implies 5x = 30 implies x = 6 hours.
