SOLUTION: 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

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?
Found 2 solutions by robertb, ankor@dixie-net.com:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let x = #minutes for Gunther, so x + 28 = #minutes for Gerta. The equation:
,
Simplifying,
,
, after combining terms and cross-multiplying.
,
,after combining terms and transposing,
(x - 84)(x + 16) = 0, after factorization.
This gives x = 84 (eliminate x = -16)
Therefore Gunther takes 84 minutes to peel a bushel of potatoes, while
Gerta can peel a bushel in 112 minutes.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
+ = 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
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