Question 653087
Let x=amount of time it takes Tom to clean the lawn working alone
Then Tom works at the rate of 1/x of the lawn per minute
x/2=amount of time it takes Butch to clean the lawn working alone
So Butch works at the rate of 1/(x/2)=2/x of the lawn per minute
Tom and Butch together work at the rate of 1/40 of the lawn per min
But together Tom and Butch work at the rate of 1/x + 2/x of the lawn per minute
So, our equation to solve is:
1/x +2/x=1/40  multiply each term by 40x
40+80=x
x=120 min-----amount of time it takes Tom working alone
x/2=120/2=60 min--------amount of time it takes Butch working alone

CK
In 40 min, Tom can do 40/120 of the lawn
In 40 min, Butch can do 40/60 of the lawn
Now if we add those together, that should equal 1 completed lawn
40/120 +40/60=1
1/3 +2/3=1
1=1

Hope this helps---ptaylor