Answer:
[tex]\frac{x-3}{3x}[/tex]
Step-by-step explanation:
Lindsay can paint 1/x of a certain room in 20 minutes.
1 hour = 3 times 20 minutes
rate of work by Lindsay in 20 minutes is [tex]\frac{3}{x}[/tex]
Let 't' be the work done by Joseph
rate of work by Joseph in 20 minutes is [tex]\frac{3}{t}[/tex]
Both completed the work in 1 hour
[tex]\frac{3}{x} +\frac{3}{t} =1[/tex]
solve the equation for 't'
Subtract 3/x on both sides
[tex]\frac{3}{t} =1-\frac{3}{x}[/tex]
[tex]\frac{3}{t} =\frac{x-3}{x}[/tex]
cross multiply it
[tex]3x=t(x-3)[/tex]
Divide both sides by x-3
[tex]\frac{3x}{x-3} =t[/tex]
Work done together is
[tex]\frac{x-3}{3x}[/tex]
