Answer
$10 \text{ minutes }$
Work Step by Step
Let $x$ be the minutes for all three to finish the work together. Expressed in $1$ unit/part, the rates are related as
\begin{array}{l}\require{cancel}
\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{60}=\dfrac{1}{x}
.\end{array}
Using the $LCD=
60x
,$ and the properties of equality, then
\begin{array}{l}\require{cancel}
60x\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{60}\right)=\left(\dfrac{1}{x}\right)60x
\\\\
3x+2x+x=60
\\\\
6x=60
\\\\
x=\dfrac{60}{6}
\\\\
x=10
.\end{array}
Hence, it takes $
10 \text{ minutes }
$ for all three to finish the work together.
