Question 766906
L BiLLy's rate
B Bobby's rate
Their combined rate 1/L+1/B=1/114 lawns per minute
Let m = minutes for Bobby to do the job himself.

Bobbys rate, {{{1/B=1/m}}}.
Billy's rate {{{1/L=1/(m-45)}}}.


Revise the rate information:
Billy's rate, {{{1/(m-45)}}} lawns per minute
Bobby's rate, {{{1/m}}} lawns per minute.


Their combined rate is given, so {{{highlight(1/(m-45)+1/m=1/114)}}}
One variable, m, so solve for m.


Simplifies to {{{m^2-27m+570=0}}}
Solution to quadratic equation gives {{{m=148}}} minutes.
Bobby's rate is one lawn mowed in 148 minutes.