Question 206336
 It takes me 4 more hours to paint room the same size of my living room than it takes my mom.
We painted the room in 5 hours together.
 If we worked independently, how long would it take to finish painting the room?
:
Let t = time required by mom
then
(t+4) = time required by me
;
Let the completed job = 1
:
{{{5/t}}} + {{{5/((t+4))}}} = 1
:
Multiply equation by t(t+4), results
5(t+4) + 5t = t(t+4)
:
5t + 20 + 5t = t^2 + 4t
:
Arrange as a quadratic on the right:
0 = t^2 + 4t - 10t - 20
:
t^2 - 6t - 20 = 0
:
Use the quadratic equation to find t
:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in the problem:
x=t: a=1; b=-6; c=-20
{{{t = (-(-6) +- sqrt(-6^2 - 4 * 1 * -20 ))/(2*1) }}}
{{{t = (6 +- sqrt(36 - (-80) ))/2 }}}
{{{t = (6 +- sqrt(36 + 80 ))/2 }}}
{{{t = (6 +- sqrt(116 ))/2 }}}
the positive solution
{{{t = (6 + 10.77 ))/2 }}}
t = {{{16.77/2}}}
t = 8.385 hr is Mom's time alone
then
8.385 + 4 = 12.385 is my time alone
:
:
Check solution:
{{{5/8.385}}} + {{{5/12.385}}} =
.596 + .404 = 1