Two masons

Two masons built the garage together—it took 18 days. If they worked independently, the other would have worked 15 days more than the first. How many days would it take each mason to build the garage alone?

Correct answer:

x =  30
y =  45

Step-by-step explanation:

$$\begin{gathered} \frac{1}{x}+\frac{1}{y}=\frac{1}{18} \\ y=x+15 \\ \frac{1}{x}+\frac{1}{x+15}=\frac{1}{18} \\ 18(2x+15)=x(x+15) \\ {x}^2-21x-270=0 \\ a=1;b=-21;c=-270 \\ D=b^2-4ac=21^2-4\cdot 1\cdot (-270)=1521 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{21\pm \sqrt{1521}}{2} \\ {x}_{1,2}=\frac{21\pm 39}{2} \\ {x}_{1,2}=10.5\pm 19.5 \\ {x}_1=30 \\ {x}_2=-9 \\ \text{ Factored form of the equation: } \\ (x-30)(x+9)=0 \\ x>0 \\ x=30 \end{gathered}$$

$y=x+15=45$

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