SOLUTION: A Master contractor and his apprentice could spackle the interior walls of a new home in 18 hours. The master contractor figures he would have finished the job himself about 5 hour

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Question 365362: A Master contractor and his apprentice could spackle the interior walls of a new home in 18 hours. The master contractor figures he would have finished the job himself about 5 hours faster than his apprentice. How long would it take each of them to complete the job solo?
If the master contractor earns $45 per hour and the apprentice earns $28.50 per hour and time is not an issue explain one way the construction company could save? Show work.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A Master contractor and his apprentice could spackle the interior walls of a new home in 18 hours.
The master contractor figures he would have finished the job himself about 5
hours faster than his apprentice.
How long would it take each of them to complete the job solo?
:
Let x = time required by the Master alone
then
(x+5) = time required by the apprentice alone
:
Let the completed job = 1
:
A typical shared work equation:
:
18%2Fx + 18%2F%28%28x%2B5%29%29 = 1
multiply equation by x(x+5), results:
18(x+5) + 18x = x(x+5)
18x + 90 + 18x = x^2 + 5x
36x + 90 = x^2 + 5x
Arrange as a quadratic equation
x^2 + 5x - 36x - 90 = 0
x^2 - 31x - 90 = 0
Solve for x using the quadratic formula: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation a=1; b=-31 c=-90
x+=+%28-%28-31%29+%2B-+sqrt%28-31%5E2-4%2A1%2A-90+%29%29%2F%282%2A1%29+
You should be able to do the math here
Your answer will be the positive solution, the Master's time alone.
:
:
If the master contractor earns $45 per hour and the apprentice earns $28.50 per hour and time is not an issue explain one way the construction company could save?
:
Multiply Master's time alone by $45, multiply the Apprentice time (5 hrs more) by 28.50, to see which would do the job cheapest.