Question 1013789
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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}}} : {{{1}}}{{{1/2}}} = {{{2/3}}} of-the-lawn-per-hour.

Let x be raking rate of her sister in the same units of {{{lawn/hour}}}.

Then their joint rate is {{{x + 2/3}}} of-the-lawn-per-hour.

The equation is 

{{{1/(x+2/3)}}} = {{{40/60}}} = {{{2/3}}},   or   ({{{40/60}}} 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 - {{{4/3}} = {{{9/3-4/3}}} = {{{5/3}}}.

Hence, x = {{{5/6}}}.

It is the sister's rate. 

Therefore, it will take {{{1/x}}} = {{{1/(5/6)}}} = {{{6/5}}} hours = 1 hour 12 minutes for the sister to rake the lawn working alone.
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