SOLUTION: a highschool hiking club held a carwash to raise money for equipment. Rudy, Cheryl, Tom and Pat volunteered to help. Rudy could wash a car in 10 minute. Cheryl in 12, Tom in 8, and

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a highschool hiking club held a carwash to raise money for equipment. Rudy, Cheryl, Tom and Pat volunteered to help. Rudy could wash a car in 10 minute. Cheryl in 12, Tom in 8, and      Log On


   

Question 103904: a highschool hiking club held a carwash to raise money for equipment. Rudy, Cheryl, Tom and Pat volunteered to help. Rudy could wash a car in 10 minute. Cheryl in 12, Tom in 8, and Pat in 15. They all started on the first car, but after 2 minutes another car came in and Pat and Tom went to work on it. one minute later Rudy quit to take care of another customer. How long did it take Cheryl to finish the first car alone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Rudy, Cheryl, Tom and Pat volunteered to help. Rudy could wash a car in 10 minute. Cheryl in 12, Tom in 8, and Pat in 15. They all started on the first car, but after 2 minutes another car came in and Pat and Tom went to work on it. one minute later Rudy quit to take care of another customer. How long did it take Cheryl to finish the first car alone.
:
Let a completed car wash = 1:
:
After the 1st two minutes, what fraction of the car was washed?
Rudy + Cheryl + Tom + Pat
2%2F10 + 2%2F12 + 2%2F8 + 2%2F15
:
Common denominator is 120:
24%2F120 + 20%2F120 + 30%2F120 + 16%2F120 = 90%2F120 = 3%2F4 of the car is washed
:
Leaving 1%2F4
Let x = time required by Cheryl to finish the job alone
:
Rudy and Cheryl + Cheryl alone
1%2F10 + 1%2F12 + x%2F12 = 1%2F4
:
The common denominator = 60; we have:
6%2F60 + 5%2F60 + 5x%2F60 = 15%2F60
:
We don't need the denominators:
6 + 5 + 5x = 15
5x + 11 = 15
5x = 15 - 11
5x = 4
x = 4%2F5 of a minute for Cheryl to finish the job
:
I'm disappointed it didn't come out in whole minutes:
:
However, checked it on a calc using .8 for 4%2F5:
2%2F10+%2B+2%2F12+%2B+2%2F8+%2B+2%2F15+%2B+1%2F10+%2B+1%2F12+%2B+.8%2F12 = 1; so I think it's right