Question 862073
The rates of each brother are added when they work on the lawn at the same time.  Use the rates as LAWNS per MINUTE.  

A, 1/something
B, {{{1/x}}} jobs per minute
A, {{{1/(x-9)}}}
A plus B, 1/20 jobs per minute, .

Note that 1 lawn is the same as 1 job.


EQUATION:
{{{1/x+1/(x-9)=1/20}}}
Solve for x, which is the time for brother B to do the 1 job alone, himself.


Multiply by x(x-9) both sides,
{{{(x-9)+x=(1/20)x(x-9)}}}
{{{2x-9=(x^2-9x)/20}}}
{{{40x-180=x^2-9x}}}
{{{x^2-9x-40x+180=0}}}
{{{x^2-49x+180=0}}}
Check discriminant, D=49^2-4*180=2401-720=1681, a positive value.
This is actually {{{highlight_green(41^2=1681)}}}, not at all obvious.
-
continuing,
{{{x=(49+sqrt(1681))/2}}}, we use the positive square root form, because it will make sense.
{{{x=(49+41)/2}}}
{{{highlight(x=45)}}}
This means, brother B mows the one lawn alone by himself in 45 minutes.