Final answer:
To find out how long it takes Cara to mow the lawn alone, we first need to determine how long it takes Craig to mow the lawn alone. Then, we can solve an equation to find the value of x, the time taken by Craig, and finally calculate 2x to find the time taken by Cara.
Step-by-step explanation:
To find out how long it takes Cara to mow the lawn alone, we first need to determine how long it takes Craig to mow the lawn alone. It is given that working together, Cara and Craig can mow the lawn in 8 hours. Let's assume that Craig takes x hours to mow the same lawn alone. Since Craig takes twice as long as Cara, we can say that Cara takes 2x hours to mow the lawn alone.
According to the given information, the work done by Cara and Craig together in one hour is equivalent to 1/8th of the entire lawn. In other words, their combined rate of work is 1/8th. We can represent Craig's rate of work as 1/x and Cara's rate of work as 1/(2x). When we add these two rates of work together, we get the combined rate, which is 1/8th.
By solving the equation (1/x) + (1/(2x)) = 1/8, we can find the value of x. Once we know the value of x, we can calculate how long it takes Cara to mow the lawn alone, which is 2 times x.