Question 726924
Think according to rates as jobs per day.  When persons do the work simultaneously, their rates are additive.


Person_______________rate in jobs per day
Joe__________________{{{1/4}}}________________
His Wife_____________{{{1/(4+1)}}}____________
Joe+Wife_____________{{{1/4+1/5}}}___________


All that is necessary to to compute the sum of the rates of Joe and his wife. Note how {{{1/(4+1)}}} is the same as {{{1/5}}}.