SOLUTION: need to write an equation and solve Nancy takes an hour and a half to rake the lawn, but it takes her only 40 minutes if her sister rakes, too. How long does it take her sister

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Question 1013789: need to write an equation and solve
Nancy takes an hour and a half to rake the lawn, but it takes her only 40 minutes if her sister rakes, too. How long does it take her sister to rake the lawn alone?
Answer by ikleyn(52781) About Me  (Show Source):
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Nancy takes an hour and a half to rake the lawn, but it takes her only 40 minutes if her sister rakes, too. How long does it take her sister to rake the lawn alone?
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Nansy's raking rate is 1 : 11%2F2 = 2%2F3 of-the-lawn-per-hour.

Let x be raking rate of her sister in the same units of lawn%2Fhour.

Then their joint rate is x+%2B+2%2F3 of-the-lawn-per-hour.

The equation is 

1%2F%28x%2B2%2F3%29 = 40%2F60 = 2%2F3,   or   (40%2F60 is 40 minutes of time in hours).

Multiply both sides by 3*(x+2/3). You will get

3 = 2*(x+2/3),   or   3 = 2x + 4/3,   or  2x = 3 - 4%2F3%7D%7D+=+%7B%7B%7B9%2F3-4%2F3 = 5%2F3.

Hence, x = 5%2F6.

It is the sister's rate. 

Therefore, it will take 1%2Fx = 1%2F%285%2F6%29 = 6%2F5 hours = 1 hour 12 minutes for the sister to rake the lawn working alone.