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

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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 )

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Adding the 2nd and 4th equations:

All 4 together can make 77 subs in 1 hour