Question 862073
A & B can mow the lawn in 20 minutes

consider mowing the lawn is one job

so they do 1/20 of the job in 1 minute


let B take x minutes to do the job alone
he does 1/x of the job in 1 minute

A takes 9 minutes less than B  (x-9)

So A does 1/(x-9) of the job in 1 minute

Together

{{{1/x + 1/(x-9) = 1/20}}}

LCM 20x(x-9)

20(x-9)+20x=x(x-9)

20x-180+20x=x^2-9x

x^2-49x+!80=0

x^2-45x-4x+!80=0

x(x-45)-4(x-45)=0

(x-45)(x-4)=0

x=45 OR 4

B takes 45 minutes to mow the lawn alone




so he does 1/9 of the job in 1 minute