# Two masons

Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himhelp?

Correct result:

x =  30
y =  45

#### Solution:

$\dfrac1x + \dfrac 1y = \dfrac{1}{18} \ \\ y = x+15 \ \\ \ \\ \dfrac1x + \dfrac{1}{x+15} = \dfrac{1}{18} \ \\ \ \\ 18(2x+15) = x(x+15) \ \\ x^2 -21x -270 =0 \ \\ \ \\ a=1; b=-21; c=-270 \ \\ D = b^2 - 4ac = 21^2 - 4\cdot 1 \cdot (-270) = 1521 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 21 \pm \sqrt{ 1521 } }{ 2 } \ \\ x_{1,2} = \dfrac{ 21 \pm 39 }{ 2 } \ \\ x_{1,2} = 10.5 \pm 19.5 \ \\ x_{1} = 30 \ \\ x_{2} = -9 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -30) (x +9) = 0 \ \\ \ \\ x > 0 \ \\ x = 30$
$y=x+15=45$

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