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
:
Change 4{{{4/5}}} 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/t}}} + {{{4.8/((t+4))}}} = 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 = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this problem: x=t; a=1; b=-5.6; c=-19.2
{{{t = (-(-5.6) +- sqrt(-4.6^2 - 4 * 1*-19.2 ))/(2*1) }}}
:
{{{t = (5.6 +- sqrt(31.36 - (-76.8) ))/(2) }}}
:
{{{t = (5.6 +- sqrt(31.36 + 76.8 ))/(2) }}}
:
{{{t = (5.6 +- sqrt(108.16))/(2) }}}
the positive solution
{{{t = (5.6 + 10.4)/(2) }}}
:
t = {{{16/2}}}
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