SOLUTION: If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long
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Question 208065This question is from textbook modern college algebra
: If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long it would take each man, working alone to complete the job?
A and B working together can do a job in 6 hours. A become ill after 3 hours of working with B, and B finished the job, continuing to work alone in 8 hours. How long would it take each working alone to do the job?
This question is from textbook modern college algebra
Found 2 solutions by ankor@dixie-net.com, vipower:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If A,B and C work together on a job, it will take 1 and 1/3 hours. If only A and B work, it would take 1 and 5/7 hours, but if B and C work, it would take 2 and 2/5 hours. How long it would take each man, working alone to complete the job?
:
Change 1 & 1/3 hrs to
Let the completed job = 1
:
Simplify the shared work equations
+ + = 1 >> + + = 1 >> + + = 3
:
convert 1 & 5/7 hrs to
+ = 1 >> + = 1 >> + = 7
:
Multiply 1st equation by 3 and subtract the 2nd equation
+ + = 9
+ + = 7
---------------------eliminates A & B, find C
= 2
12 = 2C
C = 6 hrs alone
:
The 3rd equation we can use decimal: 2 & 2/5 hrs = 2.4 hrs
+ = 1
Replace C with 6, find B
+ = 1
+ .4 = 1
= 1 -.4
= .6
.6B = 2.4
B =
B = 4 hrs alone
:
Find A, using the 2nd equation
+ = 7
+ 3 = 7
= 7 - 3
= 4
4A = 12
A = 3 hrs alone
:
:
Check solution in the 1st equation using a calc
+ + =
:
:
:
A and B working together can do a job in 6 hours. A become ill after 3 hours of working with B, and B finished the job, continuing to work alone in 8 hours. How long would it take each working alone to do the job?
:
Working the same together equation:
+ = 1
:
Working when one gets sick equation: (B works a total of 11 hrs)
+ = 1
:
Multiply the above equation by 3 and subtract the 1st equation
+ = 2
+ = 1
-----------------------------eliminates A
16B = 1
B = 16 hrs alone
:
Find A using the 1st equation
+ = 1
= -
=
Cross multiply
10A = 6 * 16
10A = 96
A = 9.6 hrs alone
;
:
Check solution on a calc using the "sick equation"
+ = 1
Answer by vipower(2) (Show Source): You can put this solution on YOUR website!
thanks a lot
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