Answer:
67.8 days
Step-by-step explanation:
We assume the problem statement is supposed to read ...
Jazz and Corbin can eat 50 pounds of peanuts in 30 days. Jazz by himself eats 50 pounds of peanuts in two weeks less time than Corbin does by himself. How many days will it take for Corbin to eat the 50 pounds of peanuts by himself?
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Let c represent the number of days it takes Corbin to eat 50 lbs of peanuts. Then c - 14 will be the number of days it takes Jazz to eat 50 lbs of peanuts. Working together, they eat 50 lbs of peanuts in 30 days, so ...
Jazz's peanuts per day + Corbin's peanuts per day = total peanuts per day
50/c + 50/(c-14) = 50/30
Multiplying by (3/5)c(c-14), we get ...
30(c -14) + 30c = c(c -14)
Subtracting the left side gives ...
c^2 -14c -60c +420 = 0
c^2 -74c +1369 = 1369 -420 . . . . subtract 420, add 1369 to complete the square
(c -37)^2 = 949 . . . . . . . . . write more compactly
c = 37 +√949 ≈ 67.8 . . . . square root and add 37
It will take 67.8 days for Corbin to eat 50 lbs of peanuts by himself.
