SOLUTION: Randy and Paul can do a piece of work in 10 days ;Randy and Guy can do it in 8 days ;Paul and Guy can do it in 12 days. How long will it take to each to do it alone ?

Question 937145: Randy and Paul can do a piece of work in 10 days ;Randy and Guy can do it in 8 days ;Paul and Guy can do it in 12 days. How long will it take to each to do it alone ?
Found 2 solutions by josmiceli, ptaylor:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Randy's rate of working
Let = Paul's rate of working
Let = Guy's rate of working
---------------------------------
Add their rates of working to get
their rate working together
(1)
(2)
(3)
-------------------------
Subtract (3) from (2)
(2)
(3)
--------------------------

Add this result to (1)

-------------------
and
(2)
(2)
(2)
---------------------
and
(1)
(1)
(1)
---------------------
check answers:
(1)
(1)
(1)
and
(2)
(2)
(2)
and
(3)
(3)
---------------------------------
I made a mistake somewhere. The method is
right, but this last step is wrong. I'm
too tired to find the problem. Just convert
fractions to mixed numbers and you
will have answers ( after finding problem )

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let R= amount of time it takes Randy to do the work alone
Then Randy works at the rate of 1/R of the job per day
Let P= amount of time it takes Paul to do the work alone
Then Paul works at the rate of 1/P of the job per day
Let G=amount of time it takes Guy to do the work alone
Then Guy works at the rate of 1/G of the job per day
Sooooo our equations to solve are:
1/R+1/P=1/10---------------------eq1
1/R+1/G=1/8------------------------eq2
1/P+1/G=1/12--------------------------eq3
Subtract eq2 from eq1 and we get:
1/P-1/G=(1/10)-(1/8)=(4/40)-(5/40)=-1/40 add this to eq3
2/P=(1/12)-(1/40)=(10/120)-(3/120)=7/120
2/P=7/120
1/P=7/240 substitute this into eq1-----------------EQ1a
1/R=(1/10)-(7/240)=(24/240)-(7/240)=17/240
1/R=17/240 substitute this into eq2-----------------EQ2a
17/240 + 1/G=1/8
1/G=(1/8)-(17/240)=(30/240)-(17/240)=13/240
1/G=13/240------------------------------------------EQ3a
From eq2a: (you can divide these out but it's easier to work in fractions when checking your work)
17R=240
R=240/17 days
From eq1a:
7P=240
P=240/7 days
From eq3a:
13G=240
G=240/13 days
CK
Randy and Paul
(17/240)+(7/240)=????1/10
24/240=1/10
1/10=1/10
Randy and Guy
(17/240)+(13/240)=????1/8
30/240=1/8
1/8=1/8
Paul and Guy
(7/240)+(13/240)=????1/12
20/240=1/12
1/12=1/12
Does this help?---ptaylor

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