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?

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) (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 4 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
:
+ = 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:

In this problem: x=t; a=1; b=-5.6; c=-19.2

the positive solution

:
t =
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
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