Hello!
The answer is:
The correct option is:
A) Jeff, 4.5 hours; Julia 9 hours.
Why?
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:
[tex]JeffRate=2JuliaRate[/tex]
Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:
[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]
Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:
[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]
[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]
[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]
[tex]3JuliaRate=\frac{1garden}{3hours}[/tex]
[tex]JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}[/tex]
We have that Julia could weed the garden by herself in 9 hours.
So, calculating how long will it take to Jeff, we have:
[tex]JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}[/tex]
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!
