SOLUTION: Tom and Butch can clean the lawn in 40 minutes if they work together. If Butch works twice as fast as Tom, how long does it take Tom to clean the lawn alone?

Question 653087: Tom and Butch can clean the lawn in 40 minutes if they work together. If Butch works twice as fast as Tom, how long does it take Tom to clean the lawn alone?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
Stan and Hilda can mow the lawn in 40 minutes if they work together. If Hilda works twice (answered by scott8148)

Stan and Hilda can mow the lawn in 40 minutes if they work together. If Hilda works twice (answered by scott8148)

Stan and Hilda can mow the lawn in 40 minutes if they work together. If Hilda works twice (answered by stanbon)

Joe and Moe can mow the lawn in 26 minutes if they work together. If Moe works twice as... (answered by nerdybill)

Sam and Dave can mow the lawn in 60 minutes if they work together. If Dave works twice as (answered by jim_thompson5910)

Stan and Hilda can mow the lawn in 60 minutes if they work together. If Hilda works twice (answered by Boreal)

Joe and Moe can mow the lawn in 32 minutes if they work together. If Moe works twice as... (answered by josgarithmetic,ikleyn,greenestamps)

Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as... (answered by funmath)

Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as (answered by stanbon)