Question

Jeff can weed the garden twice as fast as his sister Julia. Together they can weed the garden in 3 hours. How long would it take each of them working alone?
A) 4.5 hours; Julia 9 hours
B) 7.5 hours; Julia 15 hours
C) 4.5 hours; Julia 2.25 hours
D) 0.5 hours; Julia 1 hours

Answer 1

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:

$JeffRate=2JuliaRate$

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

$JeffRate+JuliaRate=\frac{1garden}{3hours}$

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

$JeffRate+JuliaRate=\frac{1garden}{3hours}$

$2JuliaRate+JuliaRate=\frac{1garden}{3hours}$

$2JuliaRate+JuliaRate=\frac{1garden}{3hours}$

$3JuliaRate=\frac{1garden}{3hours}$

$JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}$

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

$JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}$

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!