To collect data on the signal strengths in a neighborhood, Pamela must drive from house to house and take readings. She has a graduate student, Kevin, to assist her. Pamela figures it would take her 12 hours to complete the task working alone, and that it would take Kevin 20 hours if he completed the task by himself. How long will it take Pamela and Kevin to complete the task together? O 7.5 hours 8.2 hours 8.6 hours 5.5 hours

When working together, Pamela and Kevin can combine their efforts to complete the task more efficiently. Pamela's rate is \( \frac{1}{12} \) of the job per hour, and Kevin's rate is \( \frac{1}{20} \). Adding these rates together gives us their combined rate: \[ \frac{1}{12} + \frac{1}{20} = \frac{5}{60} + \frac{3}{60} = \frac{8}{60} = \frac{2}{15} \] This means together, they can complete \( \frac{2}{15} \) of the job in one hour. To find the total time \( T \) in hours taken together, we can take the reciprocal of their combined rate: \[ T = \frac{15}{2} = 7.5 \text{ hours.} \] So, it will take them 7.5 hours to complete the task together. To verify, recall that rates are additive! Sometimes people mix up the calculations by trying to directly multiply the individual times or get lost in fractions. Just remember, always convert individual times into rates per hour for clarity. It's a lot less tangled that way!