SOLUTION: If it takes workers A and B 2 days to complete a job. And it takes workers B and C 3 days to complete the same job. And it takes workers A and C 4 days to complete this job how lon
Algebra.Com
Question 407455: If it takes workers A and B 2 days to complete a job. And it takes workers B and C 3 days to complete the same job. And it takes workers A and C 4 days to complete this job how long does it take each worker to do this job alone. And what formulas are used.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If it takes workers A and B 2 days to complete a job.
And it takes workers B and C 3 days to complete the same job.
And it takes workers A and C 4 days to complete this job how long does it take
each worker to do this job alone.
:
Let a, b, c, represent the time required by each work alone
:
Let the completed job = 1
:
Write a shared work equation for each statement:
:
"If it takes workers A and B 2 days to complete a job."
+ = 1
:
"If it takes workers B and C 3 days to complete the same job."
+ = 1
:
"it takes workers A and C 4 days to complete this job"
+ = 1
:
Add all three equations to give us another equation to work with
+ + = 1
+ + = 1
+ + = 1
---------------------------------------
+ + = 3
:
Multiply the 1st equation by 3, subtract the above equation from it
+ + = 3
+ + = 3
---------------------------------------subtraction eliminates a
+ - = 0
:
=
Cross multiply
c = 7b
:
In equation: + = 1, replace c with 7b
+ = 1
Multiply by 7b, results
7(3) + 3 = 7b
21 + 3 = 7b
24 = 7b
b =
b = 3.43 hrs, B alone
:
Find c
c = 7b
c = 7(3.43)
c = 24 hrs, C alone
:
Find a using, + = 1; replace c with 24
+ = 1
multiply by 24a
24(4) + 4a = 24a
96 = 24a - 4a
96 = 20a
a =
a = 4.8 hrs, A alone
:
:
Check this in the 1st equation
+ = 1
.42 + .58 = 1 confirms our solutions of:
:
A = 4.8 hrs, B = 3.43 hrs, C = 24 hrs (almost useless)
RELATED QUESTIONS
If it takes 3 workers 15 days to complete a job, how long would it
take 5 workers to... (answered by AnlytcPhil)
A takes 20 days to complete a job X. B takes 30 days to complete the same job X. How... (answered by CubeyThePenguin)
Working together, 4 skilled workers can complete a job in 5 days. However, 5 semi-skilled (answered by ankor@dixie-net.com)
If it takes 4 workers 6 hours each to pave a road, how many hours will it take 12... (answered by amoresroy)
If it can take 10 days for 5 workers to complete a job, how long will it take 8 workers... (answered by ewatrrr)
If 15 workers can complete a job in 20 days, how long should it take 25 workers to... (answered by ankor@dixie-net.com)
Cole and Brian working together complete a job in 3 days. If it takes 9 days for Cole to... (answered by harpazo,richwmiller)
4 skilled workers can complete a job in 5 days. 5 semi-skilled workers can complete the... (answered by josgarithmetic,ikleyn)
How many workers will be needed to complete a task in 3 days, given that it takes 10 days (answered by edjones)