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Accedmychevron_right11thchevron_rightmathchevron_rightTheory Of Quadratic Functionschevron_rightExercise 3.2

Solution

Let Abdul Hadi take $x$ days to finish the work alone.

Then Abdullah takes $x+10$ days.

Work rates:

\frac{1}{x},\qquad \frac{1}{x+10}

Together they finish in 12 days:

\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}

Multiply by $12x(x+10)$ :

12(x+10)+12x=x(x+10)

24x+120=x^2+10x

x^2-14x-120=0

(x-20)(x+6)=0

Reject $x=-6$ .

\boxed{x=20}

\boxed{\text{Abdul Hadi would take 20 days.}}