Work together

Michal and Dorota would do the work together in 2.25 hours. If Dorota had to do it herself, it would have taken her 6 hours longer than Michal. Determine when Dorota will do the work herself and when Michal will do it himself.

Correct answer:

d =  9 h
m =  3 h

Step-by-step explanation:

$$\begin{gathered} 1/d+1/m=1/2.25 \\ d=6+m \\ 1/(6+m)+1/m=1/2.25 \\ m+(6+m)=m\cdot (6+m)/2.25 \\ m+(6+m)=m\cdot (6+m)/2.25 \\ -0.44444444444444m^2-0.667m+6=0 \\ 0.44444444444444m^2+0.667m-6=0 \\ a=0.444444;b=0.667;c=-6 \\ D=b^2-4ac=0.667^2-4\cdot 0.444444\cdot (-6)=11.1111111111 \\ D>0 \\ {m}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{-0.67\pm \sqrt{11.11}}{0.888889} \\ {m}_{1,2}=-0.75\pm 3.75 \\ {m}_1=3 \\ {m}_2=-4.5 \\ m>0 \\ m=m_1=3 \\ d=6+m=6+3=9\text{h} \end{gathered}$$

Our quadratic equation calculator calculates it.

$m=3=3\text{h}$

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