Answer
6 minutes
Work Step by Step
Let both mark and lynn clean the office in $T$ minutes together.
(Fraction work done in a minute by Karen)+ (Fraction work done in a minute by kim)=1
$\implies (\dfrac{1}{15}+\dfrac{1}{10})T=1$
$\implies (\dfrac{2+3}{30})T=1$
$5T=30$
or, $T=6$ minutes
