A production manager is scheduling tasks for two teams. Team A can complete a task in 4 hours, and Team B can complete the same task in 6 hours. If 'x' represents the fraction of the task Team A completes in one hour and 'y' represents the fraction of the task Team B completes in one hour, which system of equations can be used to determine their individual work rates?

Why the other options are wrong

• A. This incorrectly sets x/4 and y/6 equal to 1, implying that the rate divided by the time gives 1 task, which is mathematically unsound.
• C. This system would be used if they were working together on a task (x+y=1 if they complete 1 task together in 1 hr) or if they complete 1 task in 4 and 6 hours respectively (4x+6y=1 is incorrect). The first equation is for combined rate, not individual.
• D. This correctly represents that 'x' (rate of A) times 4 hours equals 1 whole task, and 'y' (rate of B) times 6 hours equals 1 whole task. This is equivalent to option A, but option A is a more direct answer to 'which system of equations can be used to determine their individual work rates' as it directly states the rates. However, C is also fundamentally correct and a possible interpretation. Let's re-evaluate. The question asks for 'which system of equations can be used to determine their individual work rates'. If x is the fraction of task per hour, then 4x=1 (Team A completes 1 task in 4 hours) is correct. And 6y=1 is correct. So, C is also correct. Let me check the wording and common understanding. Often, 'rate' is expressed as 'amount per unit time'. So x=1/4 is the rate. The equations 4x=1 and 6y=1 are what you solve to FIND the rate. So A is a direct statement of the rates themselves. C is the setup to find them. Given the options, A is the most direct representation of 'x represents the fraction ... Team A completes in one hour'. If x IS that fraction, then x IS 1/4. So A is better. Let's stick with A as the most direct representation of the definition of x and y.