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When A,B and C work together, they can finish installing the garden in 3 days.
The job could be completed of A worked 4 days alone and C worked 10 days alone
or if B worked 5 days alone and C worked 3 days alone.
How many days would it take each worker alone to complete the garden?
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Let "a" be the A's rate of work, in job per day;
"b" be the B's rate of work, in job per day;
"c" be the C's rate of work, in job per day.
From the condition, we have this system of 3 equations in 3 unknowns
a + b + c = , (1)
4a + 10c = 1, (2)
5b + 3c = 1. (3)
To solve, express a = from (2), and express b = from (3).
Substitute these expressions into equation (1). You will exclude "b" and "c" from (1)
and will get single equation for unknown "c"
+ + c = . (4)
Multiply both sides by 60
15(1-10c) + 12*(1-3c) + 60c = 20
15 - 150c + 12 - 36c + 60c = 20
27 - 126c = 20
27 - 20 = 126c
7 = 126c
c = = .
It means that C will complete the job in 18 days working alone.
Now a = = = = ;
b = = = = .
ANSWER. A can complete the job in 9 days working alone;
B can complete the job in 6 days working alone;
C can complete the job in 18 days working alone.
Solved.