Question 739940
Two companies working together can clear a parcel of land in 9 hours. Working alone it would take Company A 7 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?
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x=amt of time company B can clear the land alone
1/x= Its work rate
x+7=amt of time company A can clear the land alone
1/(x+7)=Its work rate
9 hrs=amt of time they can clear the land working together
1/9=their work rate
..
sum of individual work rates=work rate working together
{{{1/x+1/(x+7)=1/9}}}
LCD:9x(x+7)
{{{9(x+7)+9x=x(x+7)}}}
{{{9x+63+9x=x^2+7x}}}
{{{x^2-11x-63=0}}}
solve for x using quadratic formula
x≈-4.16 (reject, x>0)
or
x≈15.16
amt of time company B can clear the land alone≈15.16 hrs