Answer: [tex]5.73\ hours[/tex] or [tex]5\ hours\ and\ 44\ minutes[/tex]
Step-by-step explanation:
You can use the following work-rate formula:
[tex]\frac{t}{t_A}+\frac{t}{t_B}=1[/tex]
In this case let be [tex]{t_A}[/tex] the time it takes for Natalie to pick 40 bushels, [tex]{t_B}[/tex] the time it takes for Mary to pick 40 bushels and [tex]t[/tex] the time it takes to pick 40 bushels if they work together.
Based on the information given in the exercise, you can identify that:
[tex]t_A=12\\\\t_B=11[/tex]
Then, knowing this values, you need to substitute them into the formula:
[tex]\frac{t}{12}+\frac{t}{11}=1[/tex]
Finally, you must solve for "t" in order to find its value.
The result is:
[tex]t(\frac{1}{12}+\frac{1}{11})=1\\\\t(\frac{23}{132})=1\\\\t=\frac{132}{23}\\\\t=5.73\ hours[/tex]
Since [tex]1\ hour=60\ minutes[/tex]:
[tex](0.73\ hours)(\frac{60\ minutes}{1\ hour})\approx44\ minutes[/tex]
Therefore it would take 5 hours and 44 minutes to pick 40 bushels if they worked together.
