Final answer:
Jack and Ted can sweep a porch together in approximately 6.74 minutes by combining their individual work rates of 1/14 and 1/13 porches per minute, respectively.
Step-by-step explanation:
Working alone, Jack can sweep a porch in 14 minutes, and Ted can sweep the same porch in 13 minutes.
To calculate how long it would take them to sweep the porch together, we can use the concept of rates.
We compute each person's work rate per minute and then combine them to find their collective rate of work when working together.
First, we find Jack's work rate. Since Jack can complete 1 porch in 14 minutes, his work rate is 1/14 porches per minute. Similarly, Ted's work rate, since he completes the porch in 13 minutes, is 1/13 porches per minute.
Next, we add their rates together to find out their combined work rate: Jack's rate + Ted's rate
= (1/14) + (1/13) porches per minute.
To add these fractions, we need a common denominator, which would be 14*13 = 182.
Therefore, (1/14) + (1/13) = (13/182) + (14/182) = 27/182 porches per minute.
The collective work rate is 27 porches every 182 minutes. To find out how many minutes it takes them to sweep one porch together, we compute the reciprocal of this rate: 182/27 minutes per porch.
Dividing 182 by 27, we find that they can collectively sweep the porch in approximately 6.74 minutes when working together.