Final answer:
To calculate the combined time for Jack and Willie to wax a floor together, we sum their individual rates and take the reciprocal of the total rate. The correct calculation leads to approximately 5.8 minutes, which is not one of the given options, indicating a possible mistake in the options provided.
Step-by-step explanation:
The student is asking about working together rates—a typical problem in algebra and rational expressions. Jack takes 12.8 minutes to wax a floor, and Willie takes 10.6 minutes. To find out how long it would take them to wax the floor together, we first find out their individual rates of waxing a floor per minute, which are 1 floor per 12.8 minutes for Jack and 1 floor per 10.6 minutes for Willie.
The formula for work rate is work done (W) = rate (R) x time (T), which we can rearrange to find the time as T = W/R. When Jack and Willie work together, their rates add up, so their combined rate R = (1/12.8 + 1/10.6) floors per minute. We then calculate the combined time as T = 1/R to wax one floor.
Performing the calculation, R = 1/12.8 + 1/10.6 = 0.078125 + 0.09434 = 0.172465 floors per minute, and thus, T = 1/R = 1/0.172465 ≈ 5.8 minutes for them working together, which is not one of the provided options, indicating a potential typo in the original question or selections. However, if rounding the individual rates beforehand, Jack's rate would be approximately 0.0781 and Willie's rate would be approximately 0.0943, which combined would give a rate of 0.1724. When taking the reciprocal of this combined rate, we get approximately 5.8 minutes, which unfortunately still does not match the options provided. It suggests that the provided options may be incorrect or there has been a misunderstanding in the calculation process.