Answer
Maria took 17.5 hours to manicure the lawn alone.
Work Step by Step
Let $x$ hours be the time that Maria took to manicure the lawn alone, and $W$ be the total work to be done.
The work done by Mark alone in 1 hour is $\frac{1}{7}W$.
The work done by Maria alone in 1 hour is $\frac{1}{x}W$.
The work done by both of them together in 1 hour is $\frac{1}{5}W$.
Therefore,
$\frac{1}{5}W$ = $\frac{1}{7}W$ + $\frac{1}{x}W$
$\frac{1}{5}$ = $\frac{1}{7}$ + $\frac{1}{x}$
$\frac{1}{5}$ = $\frac{x + 7}{7x}$
$7x = 5x + 35$
$2x = 35$
$x = 17.5$
Hence, Maria took 17.5 hours to manicure the lawn alone.
