I need help on a word problem.

Question

Gunther and Greta can peel a bushel of potatoes in 48 minutes. Working alone, it takes Gerta 28 minutes longer than Gunther to peel potatoes. How long would it take for gunther to do this job by himself? 

Answer 1

time it takes Gunther working alone = x

time it takes Greta working alone = (x + 28)

 

1/48 = 1/x + 1/(x + 28)

 

Multiply both sides by the LCD, which is 48(x)(x + 28)

 

x(x + 28) = 48(x + 28) + 48x

x² + 28x = 48x + 1344 + 48x

x² + 28x = 96x + 1344

x² - 68x - 1344 = 0

(x + 16)(x - 84) = 0

x = -16, x = 84

 

The only solution that makes sense is x = 84 because x is a unit of time and time cannot be negative

 

Gunther can do the job alone in 84 minutes