SOLUTION: Jack and Nick have the same size lawn. Jack can mow the lawn in 24 minutes and Nick can mow the lawn in 36 minutes. At what time will Nick have twice as much lawn to mow as Jack?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jack and Nick have the same size lawn. Jack can mow the lawn in 24 minutes and Nick can mow the lawn in 36 minutes. At what time will Nick have twice as much lawn to mow as Jack?      Log On


   

Question 894645: Jack and Nick have the same size lawn. Jack can mow the lawn in 24 minutes and Nick can mow the lawn in 36 minutes. At what time will Nick have twice as much lawn to mow as Jack?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2*(1-x/24) =(1-x/36)
2-x/12 = 1-x/36
2-x/12 = 1-x/36
1-x/12=-x/36
1=-x/36+x/12
1=-x/36+3x/36
1=2x/36
1=x/18
x=18
check
Jack 2*(1-x/24) =(1-x/36) Nick
Jack 2*(1-18/24) =(1-18/36) Nick
Jack 2*(6/24) =(18/36) Nick
Jack 12/24 =18/36 Nick
Jack 1/2 =1/2 Nick
ok

check
Jack (1-x/24) (1-x/36) Nick
Jack (1-18/24) (1-18/36) Nick
Jack (1-3/4) (1-1/2) Nick
Jack (6/24) (18/36) Nick
Jack 1/4 1/2 Nick
ok
After 18 minutes Jack will have finished 3/4 and have 1/4 left
After 18 minutes Nick will have finished 1/2 and have 1/2 left

see also http://www.algebra.com/algebra/homework/equations/Equations.faq.question.829787.html
http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.824795.html