SOLUTION: Jose and Carl can retile a roof in 10 h. Working alone, Jose could do the job 4.5 h faster than Carl. How long would each man need to do the job by himself?

Question 116058: Jose and Carl can retile a roof in 10 h. Working alone, Jose could do the job 4.5 h faster than Carl. How long would each man need to do the job by himself?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jose and Carl can re-tile a roof in 10 h. Working alone, Jose could do the job 4.5 h faster than Carl. How long would each man need to do the job by himself?
:
Let x = time required if J works by himself
Then
(x+4.5) = time required if C works by himself
:
Let the completed job = 1
:
+ = 1
:
If we multiply the equation by x(x+4.5) we can get rid of the denominators
10(x+4.5) + 10x = x(x+4.5)(1)
:
10x + 45 + 10x = x^2 + 4.5x
:
20x + 45 = x^2 + 4.5x
:
0 = x^2 + 4.5x - 20x - 45
:
A quadratic equation:
x^2 - 15.5x - 45 = 0
:
Use the quadratic formula to solve this. a=1; b=-15.5; c=-45
:
the positive solution should be x = 18 hrs is time for J working alone
Then
18 + 4.5 = 22.5 hrs for C working alone
;
:
Check solutions:
+ = 1
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