SOLUTION: 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 the sister to rake the lawn alone? Answer: l hour

Question 25656: 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 the sister to rake the lawn alone?
Answer: l hour and 12 minutes. BUT HOW DO I GET THAT!! Been trying for 3 days!
THANKS
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Work done = (rate)(time)
Nancy rate is 1/(3/2)=(2/3)job/hr.
Let Sister's time to do the job be "x"; then her rate is 1/x.
Note that 40min.= 2/3 hr.
EQUATION:
Working together their rate is (2/3+1/x)job/hr.
Amount of time to do job together is 2/3 hr.
(2/3 + 1/x)(2/3) = 1
(2/3 + 1/x)= 3/2
(2x+3)/3x =3/2
4x+6=9x
5x=6
x=1 1/5 = 1hr + (1/5)hr. = 1 hr. + 12 min.
Cheers,
Stan H.
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