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`

Explanation:

You can use the following work-rate formula:

`(t)/(t_A)+(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:

`(t)/(12)+(t)/(11)=1`

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

The result is:

`t((1)/(12)+(1)/(11))=1\\\\t((23)/(132))=1\\\\t=(132)/(23)\\\\t=5.73\ hours`

Since
`1\ hour=60\ minutes`:

`(0.73\ hours)((60\ minutes)/(1\ hour))\approx44\ minutes`

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