Question 319516
It takes one employee 3 hours longer to mow a football field than it does a more experienced employee.
 Together they can mow the grass in 2 hours. How long does it take for each 
person to mow the football field working alone?
:
Assume they each have a mower
:
Let t = time required by the experienced employee alone
then
(t+3) = time for the other employee
:
Let the completed job = 1 
:
A shared work equation
{{{2/t}}} + {{{2/((t+3))}}} = 1
multiply by t(t+3), results:
2(t+3) + 2t = t(t+3)
:
2t + 6 + 2t = t^2 + 3t
combine like terms on the right
0 = t^2 + 3t - 4t - 6
A quadratic equation
t^2 - t - 6 = 0
Factors to
(t - 3)(s + 2) = 0
positive solution
t = 3 hrs for the experienced guy by himself
and
3 + 3 = 6 hrs for the other guy by himself
:
:
Check solution
{{{2/3}}} + {{{2/6}}} = 
{{{2/3}}} + {{{1/3}}} = 1