Question

Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours

Answer 1

Hi there!

Say h = hours spent. We know Rachel finishes the job in 5 hours, thus, she finishes $\frac{1}{5}$ of the job in one hour. We also know Carl finishes the job in 8 hours, thus, he finishes $\frac{1}{8}$ of the job in one hour. Working together, this would equal:

$\frac{1}{5}+\frac{1}{8}$

$\frac{8}{40}+\frac{5}{40}$

$\frac{13}{40}$

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.

$\frac{13}{40}h=1$

$h=\frac{40}{13}$

$h\approx 3.0769$

Thus, it will take them approximately 3.0769 hours, or approximately 3 hours  4.614 minutes to finish the job together.