Cindy and Jim, working together, can weed the garden in 6
hours. Working alone, Jim takes twice as long as Cindy. How long does it take Cindy to weed the garden alone?
Let's say Cindy takes x hours to weed the garden alone. Then Jim takes 2x hours to weed the garden alone.
Working together, they can weed the garden in 6 hours, so their combined work rate is:
1/6 = (1/x) + (1/2x)
To solve for x, we can multiply both sides by 6x:
x = 3
Therefore, it takes Cindy 3 hours to weed the garden alone.
Let's assume that Cindy takes "x" hours to weed the garden alone. Since Jim takes twice as long as Cindy, we can say that Jim takes 2x hours to weed the garden alone.
When they work together, their rates add up. So, Cindy's rate is 1/x of the garden per hour and Jim's rate is 1/(2x) of the garden per hour.
When they work together, their combined rate is 1/6 of the garden per hour because they can complete the entire garden in 6 hours.
Using this information, we can create the equation:
1/x + 1/(2x) = 1/6
To solve this equation, we can multiply every term by 6x to get rid of the denominators:
6 + 3 = x
Simplifying the equation:
9 = x
So, Cindy takes 9 hours to weed the garden alone.