SOLUTION: alan, bill, cathy, and debbie work at a sub shop. It takes alan 2 minutes to make 1 sub alone. When working together , alan and bill can make 5 subs in 6 minutes, bill and cathy ca

Question 1003343: alan, bill, cathy, and debbie work at a sub shop. It takes alan 2 minutes to make 1 sub alone. When working together , alan and bill can make 5 subs in 6 minutes, bill and cathy can make 7 subs in 12 mintues, and cathy and debbie can make 9 subs in 20 minutes. If all four employees work together , how many subs can they make in an hour?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
alan, bill, cathy, and debbie work at a sub shop.
let a = Alan's time to make one sub
let b = Bill's time to make one sub
let c = Cathy's time " "
let d = Debbie's time " "
:
It takes alan 2 minutes to make 1 sub alone.
a = 2
When working together , alan and bill can make 5 subs in 6 minutes,
+ = 5
so we have
+ = 5
3 + = 5
= 5 - 3
= 2
2b = 6
b = 3 min for bill to make 1 sub
:
bill and cathy can make 7 subs in 12 mintues, and
+ = 7
+ = 7
= 7 - 4
= 3
3c = 12
c = 4 min for Cathy to make 1
:
cathy and debbie can make 9 subs in 20 minutes.
+ = 9
+ = 9
= 9 - 5
= 4
4d = 20
d = 5 min for Debbie to make 1
:
If all four employees work together , how many subs can they make in an hour?
All 4 in 60 min
+ + + =
replace the values for each
+ + + =
30 + 20 + 15 + 12 = 77 subs
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let their rates of working = Ra, Rb, Rc, and Rd
( he makes 1 sub in 2 min )

---------------------
Adding the 2nd and 4th equations:

All 4 together can make 77 subs in 1 hour
RELATED QUESTIONS
Alan and Gary,working together, can complete a job in 36 minutes. Working alone, Alan... (answered by richwmiller)
Alan, Betty, and Cathy each have the same amount of money. How much money should Betty... (answered by ikleyn)
Alan, Betty, and Cathy each have the same amount of money. How much money should Betty... (answered by ikleyn)
Alan can do a piece of work in 15 days; Bill can do it in 20 days. If Alan works alone on (answered by josmiceli)
Tracey and Alan publish a 10-page independent newspaper once a month. At production, Alan (answered by w_parminder)
Hi bob takes 4 hours to clean a room. Alan takes 2 hours. If bob started at 3pm and... (answered by greenestamps,josgarithmetic,ikleyn)
Alan and Jim were asked by their boss to work on a project. Since Jim had to visit a... (answered by mukhopadhyay)
Pls help me solve this word problem: Two men paint a home. Jim can paint it alone in 5... (answered by lwsshak3)
Q Alan and Bob walk from school to the library. Alan takes 40 minutes while Bob takes 20 (answered by ikleyn)