Joe can weed the garden twice as fast as his sister Janet. Together they can weed the garden in 2 hours. How long would it take each of them working alone? A:(1)/(x)

Question

Joe can weed the garden twice as fast as his sister Janet. Together they can weed the garden in 2 hours. How long would it take each of them working alone?

A:
`(1)/(x)`

Answer 1

Joe: 3 hrs

Janet: 6hrs

Explanation:

joe takes x hours

so in 1 hr he does 1/x of the garden

janet takes 2x hours

so in 1 hr she does 1/(2x) of the garden

In one hour together they do 1/2 of the garden

1/x + 1/(2x) = 1/2

2/(2x) + 1/(2x) = 1/2

3/(2x) = 1/2

Cross multiply

6 = 2x

x = 3

Joe: 3 hrs

Janet: 6hrs