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Answer:
28 hours
Step-by-step explanation:
Let x represent Jack's time. Then Jill's is x-7. Together their rate of carrying water in hills per hour is ...
1/x + 1/(x -7) = 1/12
Multiplying by 12x(x -7) gives ...
12(x -7) +12x = x(x -7)
x^2 -31x +84 = 0 . . . . . subtract the left side and simplify
(x -3)(x -28) = 0 . . . . . . . . . . factor
x = 3 or x = 28 . . . . . . . . . . x-values that make the factors zero
We know the times must be longer than 12 hours, so the value x=3 is extraneous for this problem.
It takes Jack 28 hours to carry the cooler of water up the hill working alone.
