You are mowing the lawn of a large house. The whole job consists of two parts: the front yard and the back yard. The front takes twice as long as the back. What fraction of the whole job is the back? Use the following notation:

Question

Let w = time for whole job.
Let x = time for back lawn.
Use this notation to develop an algebraic equation to solve the problem. Carefully check your result to make sure it satisfies the given condition. Your instructor will provide the correct solution.

Answer 1

Solution of First Problem
Use the given notation to form an equation showing the whole job consists of two parts:
x = back
2x = front (because front is twice the back)
w = whole job (the sum of the both parts)
Thus: w = x + 2x adding gives w. = 3x
From this equation you can see that the whole job take 3 times as long as the back alone. Thus, the back is 1/3 the whole job. You can see this more clearly by dividing both sides of the equation by three:
Start with the equation above w = 3x
Divide both sides by 3 to get a new equation w / 3 = 3x / 3
Remove 3 / 3 since it is one, leaving x
Express the final equation in English

"One-third of the whole job is equal to the time for the back alone."