Answer:
6.5 hours to the nearest tenth
Step-by-step explanation:
Brenda takes 14 hours to pick 40 apples, so her rate is ![\frac{1}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B14%7D)
Ted can also pick 40 apples in 12 hours, Ted's rate is ![\frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D)
The combined rate of Brenda and Ted is
...eqn1
Let
represent how long it would take if they worked together.
Their rate of working together in terms of y is
...eqn2
Equations (1) and (2) are equal.
This implies that:
![\frac{1}{y}=\frac{1}{14}+\frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7By%7D%3D%5Cfrac%7B1%7D%7B14%7D%2B%5Cfrac%7B1%7D%7B12%7D)
![\frac{1}{y}=\frac{13}{84}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7By%7D%3D%5Cfrac%7B13%7D%7B84%7D)
![y=\frac{84}{13}=6.46}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B84%7D%7B13%7D%3D6.46%7D)
Therefore it would take approximately 6.5 hours if they work together