Question 944677
Let b = time billy takes to mow the lawn alone.
Let B = time Bobby takes to mow the lawn alone.
The formula for the time it takes for them to work together is given by
(1) {{{ T = 1/(1/b+1/B)}}} which reduces to
(2) {{{ T = (b*B)/(b+B)}}}
We are given that
(3) T = 65 and
(4) b = B - 30
Substitute (3) and (4) into (2) and get
(5) {{{65 = ((B-30)*B)/(B-30+B)}}} which simplifies to
(6){{{B^2 -160B+1950 = 0 }}}
Use the quadratic equation to determine the two roots of (6) as
(7){{{ B = 80 +- sqrt(4450)}}}
Choose the positive square root because the negative square root makes b, which is 30 less than B, a negative time.
Therefore
(8) {{{ B = 80 + sqrt(4450)}}} or
B is approximately 146.708 minutes.
Then b 1s approximately 116.708 minutes.
Substituting these values into (2) gives 
(9) T = (116.708*146.708)/(116.708+146.708) or
(10) T = 64.9998
Answer: Bobby takes about 146.7 minutes to mow the lawn alone.