Question 374130
Together Gunther and Gerta can peel a bushel of potatoes in 48 minutes.
 Working alone, it takes Gerta 28 minutes longer than Gunther to peel a bushel of potatoes. 
How long would it take for Gunther to do this job by himself?
:
Let g = Gun's time alone
then
(g+28) = Gert's time alone
:
Let the completed job = 1
:
A typical shared work equation, each will do a fraction of the job, the two fractions add up to 1.
:
{{{48/g}}} + {{{48/((g+28))}}} = 1
Multiply by g(g+28) results:
48(g+28) + 48g = g(g+28)
:
48g + 1344 + 48g = g^2 + 28g
:
96g + 1344 = g^2 + 28g
Arrange as a quadratic equation on the right:
0 = g^2 + 28g - 96g - 1344
:
g^2 - 68g - 1344 = 0
you can use the quadratic formula to find g, but this will factor to:
(g-84)(g+16) = 0
The positive solution
g = 84 minutes, Gun's time alone
;
:
Check solution
48/84 + 48/112 = 
.57 + .43 = 1.00, confirms our solution