Answer: It would it take 7.5h for Stan to do it alone.
Explanation
Given
• Stan and Eli can mow a lawn in 3 hours.
,• It would take Eli 5 hours to do it alone.
,• How long would it take Stan alone?
Procedure
Eli does 1/5 of the work per hour, while Stan and Eli do 1/3 of the work per hour. Assuming that their per-hour rates are additive (they never get in each other's way), we can build the following relation, in which t is the time of Stan doing it alone:
[tex]\frac{1}{t}+\frac{1}{5}=\frac{1}{3}[/tex][tex]\frac{1}{t}=\frac{1}{3}-\frac{1}{5}[/tex][tex]\frac{1}{t}=\frac{5-3}{15}[/tex][tex]\frac{1}{t}=\frac{2}{15}[/tex]Getting the reciprocal of both sides:
[tex]\frac{t}{1}=\frac{15}{2}[/tex][tex]t=\frac{15}{2}\approx7.5h[/tex]