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

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(52785) (Show Source): You can put this solution on YOUR website!
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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  :  =  of-the-lawn-per-hour.

Let x be raking rate of her sister in the same units of .

Then their joint rate is  of-the-lawn-per-hour.

The equation is 

 =  = ,   or   ( 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 -  = .

Hence, x = .

It is the sister's rate. 

Therefore, it will take  =  =  hours = 1 hour 12 minutes for the sister to rake the lawn working alone.

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