To determine how long does it take the chef to make the dessert:
let the assistant takes = x minutes
assistant does in one minute = 1/x
chef takes = x - 6 minutes
chef does in one minute = 1/(x-6)
both does in one minute
[tex]\begin{gathered} \frac{1}{x}+\frac{1}{x-6} \\ \frac{x-6+x}{x(x-6)}=\frac{2x-6}{x^2-6x} \end{gathered}[/tex]both does complete work in x(x-6)/(2x-6) minutes
[tex]\begin{gathered} 47(x-6)=x^2-6x \\ 47x-282=x^2-6x \\ x^2-6x-47+282=0 \\ x^2-53x+282=0 \\ x=\frac{53+41}{2}=\frac{94}{2}\text{minutes=47minutes} \\ x=\frac{53-41}{2}=\frac{12}{2}\text{minutes}=\text{ 6minutes cannot be 6} \end{gathered}[/tex]Therefore it took them with assistant = 47 minutes
Hence it took the chef 47 - 6 minutes = 41 minutes
