SOLUTION: I don't know how to set up the equation for this word problem... My cat Archimedes can rid my garage of mice twice as fast as my neighbor's cat, Pythagoras. If they joined forc

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I don't know how to set up the equation for this word problem... My cat Archimedes can rid my garage of mice twice as fast as my neighbor's cat, Pythagoras. If they joined forc      Log On


   

Question 372353: I don't know how to set up the equation for this word problem...
My cat Archimedes can rid my garage of mice twice as fast as my neighbor's cat, Pythagoras. If they joined forces, they can clear a garage in a mere two hours. In how many hours does it take for each of these felines to clear a garage of mice working alone?
I think the known values are:
Pythagoras's rate = x
Archimedes' rate = 2x
Total time working together = 2 hours
Thank you!
Found 3 solutions by stanbon, mananth, scott8148:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
My cat Archimedes can rid my garage of mice twice as fast as my neighbor's cat, Pythagoras. If they joined forces, they can clear a garage in a mere two hours. In how many hours does it take for each of these felines to clear a garage of mice working alone?
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Let Arch time = x hrs/job ; Arch rate = 1/x job/hr
Pyth time = 2x hrs/job ; Pyth rate = 1/(2x) job/hr
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Together time = 2 hr/job ; together rate = 1/2 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(2x) = 1/2
2 + 1 = x
---
Arch time = x = 3 hrs
Pyth time = 2x = 6 hrs.
===========================
Cheers,
Stan H.

Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Pythagoras's rate = x
Archimedes' rate = 2x
Total time working together = 2 hours
...
I will continue your steps
..
Pythagoras's can do 1/x of the job in 1 hour
Archimedes' can do 1/ 2x of the job in 1 hour.
...
together they can do 1/x + 1/2x of the job in 1 hour
(2+1)/2x
=2+1/2x
=3/2x
So they will take 2x/3 hours to do the job. = 2
2x/3=2
multiply by 3
2x = 6
/2
x=3 Pythagoras's time
2x= 6 hours = Archimedes
..
so you know how many hours they take
...
m.ananth@hotmail.ca

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
they each do some FRACTION of the job , based on their individual times
___ the fractions sum to one (the WHOLE job)

(2hr / A) + (2hr / P) = 1

Pythagoras' time is twice Archimedes' ___ P = 2A

substituting ___ (2 / A) + (2 / 2A) = 1 ___ 3hr = A

substituting ___ P = 2(3) = 6hr