Question 741429
The rate is as "mow the lawn" in number of minutes, jobs per minute.


Andy+Brian, rate is 1 job per 30 minutes, or 1/30 job/min.

Andy, rate is unknown 1/(w) job/min, where w is the time it takes Andy to do one job.

Brian, rate is 1/(11+w), because, "11 minutes more than it takes andy."


The rates of each brother are additive when they work together, and we have THAT value.
{{{highlight(1/w+1/(11+w)=1/30)}}}
Remember, w is a quantity of minutes.

 
Multiplying both sides of the equation by 30w(11+w),
{{{30(w+11)+3w=w^2+11w}}}
{{{30w+330+3w=w^2+11w}}}
{{{33w+330=w^2+11w}}}
{{{w^2-22w-330=0}}}


Solution to Quadratic Formula: {{{w=(22+sqrt(22^2-4*(-330)))/2}}}
{{{highlight(w=32)}}} minutes.


RESULT: Andy does the job in 32 minutes, and Brian does the job in 43 minutes.