<h2>
Hello!</h2>
The answer is:
The correct option is:
A) Jeff, 4.5 hours; Julia 9 hours.
<h2>Why?</h2>
To solve the problem, we need to write two equations using the given information.
So, writing the first equation we have:
We know that Jeff can weed the garden twice as fas as his sister Julia, so:
![JeffRate=2JuliaRate](https://tex.z-dn.net/?f=JeffRate%3D2JuliaRate)
Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:
![JeffRate+JuliaRate=\frac{1garden}{3hours}](https://tex.z-dn.net/?f=JeffRate%2BJuliaRate%3D%5Cfrac%7B1garden%7D%7B3hours%7D)
Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:
![JeffRate+JuliaRate=\frac{1garden}{3hours}](https://tex.z-dn.net/?f=JeffRate%2BJuliaRate%3D%5Cfrac%7B1garden%7D%7B3hours%7D)
![2JuliaRate+JuliaRate=\frac{1garden}{3hours}](https://tex.z-dn.net/?f=2JuliaRate%2BJuliaRate%3D%5Cfrac%7B1garden%7D%7B3hours%7D)
![2JuliaRate+JuliaRate=\frac{1garden}{3hours}](https://tex.z-dn.net/?f=2JuliaRate%2BJuliaRate%3D%5Cfrac%7B1garden%7D%7B3hours%7D)
![3JuliaRate=\frac{1garden}{3hours}](https://tex.z-dn.net/?f=3JuliaRate%3D%5Cfrac%7B1garden%7D%7B3hours%7D)
![JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}](https://tex.z-dn.net/?f=JuliaRate%3D%5Cfrac%7B1garden%7D%7B3hours%2A3%7D%3D%5Cfrac%7B1garden%7D%7B9hours%7D)
We have that Julia could weed the garden by herself in 9 hours.
So, calculating how long will it take to Jeff, we have:
![JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}](https://tex.z-dn.net/?f=JeffRate%3D2%2AJuliaRate%5C%5C%5C%5CJeffRate%3D2%2A%5Cfrac%7B1garden%7D%7B9hours%7D%3D%5Cfrac%7B2garden%7D%7B9hours%7D%3D%5Cfrac%7B1garden%7D%7B4.5hours%7D)
We have that Jeff could weed the same garden by himself in 4.5 hours.
Hence, the correct option is:
A) Jeff, 4.5 hours; Julia 9 hours.
Have a nice day!