Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker?

Answer 1

rate of one worker --- 1/x
rate of the other ---- 1/(x+10)

1/x + 1/(x+10) = 1/12
times 12x(x+10)

12(x+10) + 12x = x(x+10)
12x + 120 + 12x = x^2 + 10x
x^2 - 14x - 120 = 0
(x - 20)(x + 6) = 0
x = 20 or x = -6, clearly x > 0

State your conclusion.