Question

Natalie picks 40 bushels in 12 hours and Mary can pick the same amount in 11 hours. how long would it take if they worked together?

Answer 1

Answer: $5.73\ hours$ or $5\ hours\ and\ 44\ minutes$

Step-by-step explanation:

You can use the following work-rate formula:

$\frac{t}{t_A}+\frac{t}{t_B}=1$

In this case let be ${t_A}$ the time  it takes for Natalie to pick 40 bushels, ${t_B}$ the time it takes for Mary to pick 40 bushels and $t$ the time it takes to pick 40 bushels  if they work together.

Based on the information given in the exercise, you can identify that:

$t_A=12\\\\t_B=11$

Then, knowing this values, you need to substitute them into the formula:

 $\frac{t}{12}+\frac{t}{11}=1$

Finally, you must solve for "t" in order to find its value.

The result is:

$t(\frac{1}{12}+\frac{1}{11})=1\\\\t(\frac{23}{132})=1\\\\t=\frac{132}{23}\\\\t=5.73\ hours$

Since $1\ hour=60\ minutes$:

$(0.73\ hours)(\frac{60\ minutes}{1\ hour})\approx44\ minutes$

Therefore it would take 5 hours and 44 minutes  to pick 40 bushels if they worked together.