SOLUTION: Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 and 4/5 days. How long would each of them take to frame the cabin alone?

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Question 203099: Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 and 4/5 days. How long would each of them take to frame the cabin alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Lee can frame a cabin in 4 days less than Ron.
When they work together, they will do the job in 4 and 4/5 days.
How long would each of them take to frame the cabin
:
Change 44%2F5 to 4.8
:
Let t = time required by Lee to do the job
then
(t+4) = time required by Ron
:
Let the completed job = 1
:
4.8%2Ft + 4.8%2F%28%28t%2B4%29%29 = 1
Multiply by t(t+4) to get rid of the denominators, results:
4.8(t+4) + 4.8t = t(t+4)
:
4.8t + 19.2 + 4.8t = t^2 + 4t
:
9.6t + 19.2 = t^2 + 4t
:
0 = t^2 + 4t - 9.6t - 19.2
a quadratic equation
t^2 - 5.6t - 19.2 = 0
:
Use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem: x=t; a=1; b=-5.6; c=-19.2
t+=+%28-%28-5.6%29+%2B-+sqrt%28-4.6%5E2+-+4+%2A+1%2A-19.2+%29%29%2F%282%2A1%29+
:
t+=+%285.6+%2B-+sqrt%2831.36+-+%28-76.8%29+%29%29%2F%282%29+
:
t+=+%285.6+%2B-+sqrt%2831.36+%2B+76.8+%29%29%2F%282%29+
:
t+=+%285.6+%2B-+sqrt%28108.16%29%29%2F%282%29+
the positive solution
t+=+%285.6+%2B+10.4%29%2F%282%29+
:
t = 16%2F2
t = 8 days, Lee working alone
and
8 + 4 = 12 days, Ron alone
:
:
Check solution in original work equation
4.8/8 + 4.8/12 =
.6 + .4 = 1