SOLUTION: When Amos and Bert do a certain job, it takes 13 and 19/23 hours. WHen Bert and Clyde do it, it takes 13 and 1/5 hours. When Amos and Clyde do it, it takes 17 and 5/23 hours. How l
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-> SOLUTION: When Amos and Bert do a certain job, it takes 13 and 19/23 hours. WHen Bert and Clyde do it, it takes 13 and 1/5 hours. When Amos and Clyde do it, it takes 17 and 5/23 hours. How l
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Question 451900: When Amos and Bert do a certain job, it takes 13 and 19/23 hours. WHen Bert and Clyde do it, it takes 13 and 1/5 hours. When Amos and Clyde do it, it takes 17 and 5/23 hours. How long does it take each brother to do it alone? Found 3 solutions by robertb, stanbon, josmiceli:Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!
Subtracting the 2nd equation from the 1st, we get .
Adding the previous equation to the 3rd equation gives .
==> ==> hours.
You can now get the values for b and c.
You can put this solution on YOUR website! When Amos and Bert do a certain job, it takes 13 and 19/23 hours.
A + B + 0 = 23/318
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WHen Bert and Clyde do it, it takes 13 and 1/5 hours.
0 + B + C = 5/66
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When Amos and Clyde do it, it takes 17 and 5/23 hours.
A + 0 + C = 23/396
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How long does it take each brother to do it alone?
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Solve the system of three equations to get each person's work rate:
A rate = 0.027325; Then A's time to do the job = 1/0.027325 ~ 36.6 hrs
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B rate = 0.045002; Then B's time to do the job = 1/0.045002 ~ 22.22 hrs
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C rate = 0.030756; Then C' time to do the job = 1/0.030756 ~ 32.51 hrs
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Cheers,
Stan H.
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You can put this solution on YOUR website! Time for A and B:
(1) hrs
Time for B and C:
(2) hrs
Time for A and C:
(3) hrs
--------------
(1)
(1)
(1)
--------------
(2)
(2)
--------------
(3)
(3)
(3)
---------------
Let their rates of working = , , and
given:
(1)
(2)
(3)
Note that the right sides mean ( 1 job) / ( time to do that job)
This is 3 equations and 3 unknowns, so it's solvable
Subtract (3) from (1)
(1)
(3)
-----------------------
Add this to (2)
(2)
and
(2)
(