Question

1. When Jack and Jill work together, they can carry a cooler of

water up a hill in 12 hours. When Jill works alone it takes her
7 fewer hours than when Jack works alone. How long would it
take Jack, working alone, to carry a cooler of water up a hill?

Answer 1

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Answer:

28 hours

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.