Hi there!
Say h = hours spent. We know Rachel finishes the job in 5 hours, thus, she finishes [tex]\frac{1}{5}[/tex] of the job in one hour. We also know Carl finishes the job in 8 hours, thus, he finishes [tex]\frac{1}{8}[/tex] of the job in one hour. Working together, this would equal:
[tex]\frac{1}{5}+\frac{1}{8}[/tex]
[tex]\frac{8}{40}+\frac{5}{40}[/tex]
[tex]\frac{13}{40}[/tex]
Now, this is the rate per hour. Thus, multiply this by h to get how much of the work is done in terms of hours spent, and set it to 1 to find how many hours it would take to finish 100% of the job.
[tex]\frac{13}{40}h=1[/tex]
[tex]h=\frac{40}{13}[/tex]
[tex]h\approx 3.0769[/tex]
Thus, it will take them approximately 3.0769 hours, or approximately 3 hours 4.614 minutes to finish the job together.
