SOLUTION: Tom and the Felix working together can paint 16 walls per hour. Felix and the Sue can paint 18 walls between them in an hour. Tom and the Sue can combine their labours to paint 1

Question 948479: Tom and the Felix working together can paint 16 walls per hour.
Felix and the Sue can paint 18 walls between them in an hour.
Tom and the Sue can combine their labours to paint 10 walls per hour.
132 walls need to be painted, so how long would it take to accomplish this if all three worked together?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Tom and the Felix working together can paint 16 walls per hour.
Felix and the Sue can paint 18 walls between them in an hour.
Tom and the Sue can combine their labours to paint 10 walls per hour.
132 walls need to be painted, so how long would it take to accomplish this if all three worked together?
----
Tom + Felix rate:: 1/16 wall/hr
Felix + Sue rate:: 1/18 wall/hr
Tom and Sue rate:: 1/10 wall/hr
----
t + f = 1/16
s + f = 1/18
----
Subtract to get::
t-s = 1/16- 1/18 = 2/(16*18) = 1/144
---
t+s = 1/10
---
Add to get
2t = (1/144)+ 1/10
2t = 154/1440
t = 77/1440 (Tom's rate)
---
f = 1/16 - (77/1440) = (1440-16*77)/(16*1440) = 208/23040 (Felix's rate)
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s + (208/23040) = 1/18
s = 0.04653 (Sue's rate
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Equation:
x(0.04653 + 0.00903 + 0.05347) = 32
x = 293.5 hrs
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Note:: Check the arithmetic.
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Cheers,
Stan H.
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