Mike takes 75 minutes to paint the room. So, in 1 minute the fraction of the room Mike paints is [tex] \frac{1}{75} [/tex].
Likewise, in 1 minute the fraction of the room Joan paints is [tex] \frac{1}{60} [/tex].
Lastly, in 1 minute the fraction of the room Kyle paints is [tex] \frac{1}{80} [/tex].
Now, let [tex] t [/tex] be the number of minutes taken to paint the whole room when all three are working together.
Then, in 1 minute the fraction of the room the three paint will be [tex] \frac{1}{t} [/tex].
This can be written as:
[tex] \frac{1}{t}=\frac{1}{75}+\frac{1}{60}+\frac{1}{80}=\frac{17}{400} [/tex]
Therefore, If all three work together then they will finish the room in:
[tex] t=\frac{400}{17}\approx 23.53 minutes [/tex]
