we are given
Mark clean his father's office in 30 minutes
so, the amount of work done by Mark in 1 minute is [tex] \frac{1}{30} [/tex]
younger sister Lynn can clean the office in 40 minutes
so, the amount of work done by younger sister Lynn in 1 minute is [tex] \frac{1}{40} [/tex]
total work done by them in 1 minute is [tex] \frac{1}{30}+\frac{1}{40} [/tex]
now, we can simplify it
[tex] =\frac{4*1}{4*30}+\frac{3*1}{3*40} [/tex]
[tex] =\frac{4+3}{120} [/tex]
[tex] =\frac{7}{120} [/tex]
total time taken to complete same work is [tex] \frac{120}{7} min [/tex]........Answer
