Answer : The time taken to clean the apartment when they work together is, 2.73 hours.
Step-by-step explanation :
Let the time taken to clean the apartment be, 'x' hours
As we are given that Mary can clean her apartment in 6 hours and her roommate can clean the apartment in 5 hours. The work is same.
Amount of work done by Mary :
Amount of work done in 1 hour = [tex]\frac{1}{6}[/tex]
Amount of work done in 'x' hour = [tex]\frac{x}{6}[/tex]
Amount of work done by roommate :
Amount of work done in 1 hour = [tex]\frac{1}{5}[/tex]
Amount of work done in 'x' hour = [tex]\frac{x}{5}[/tex]
As the work is same. That means, the amount of work done is, 1.
Now we have to determine the time taken to clean the apartment when they work together.
[tex]\frac{x}{6}+\frac{x}{5}=1[/tex]
By solving the term 'x', we get:
[tex]\frac{(5+6)x}{30}=1[/tex]
[tex]x=\frac{30}{11}[/tex]
[tex]x=2.73hours[/tex]
Thus, the time taken to clean the apartment when they work together is, 2.73 hours.
