Suppose the whole job has three parts: front, back, and side. If the back takes twice as long as the side and the front takes twice as long as the back, what fraction of the whole job is the side?
Notation: w = time for whole job; x --- time for side lawn.
Use the given notation to form an equation showing the whole job consists of three parts:
x = side
2x = back (because back is twice the side) 4x = front (because front is twice the back) w = whole job (the sum of the three parts)
Thus: w = x + 2x + 4x adding gives w = 7x
From this equation you can see that the whole job take 7 times as long as the back alone. Thus, the back is 7 of the whole job. You can see this more clearly by dividing both sides of the equation by seven:
Start with the equation above w =7x
Divide both sides by 7 to get a new equation w/7 =7x /7
Remove 7 / 7 since it is one, leaving 7w—x
Express the final equation in English
"One-seventh of the whole job is equal to the time for the side alone."
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