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James, Karen, and Lou are hiking. Lou forgot to bring any water. James brought 2 gallons of water and Karen brought 1\34 gallons of water. The three of them agree to divide all the water equally among them. Lou gives $2 for the water he receives, which James and Karen agree to divide fairly between the two of them. How much money should James receive?

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sqdancefan

Answer:

  $1.20

Step-by-step explanation:

We assume that Karen brought 1 3/4 gallons, or 7/4 gallons. James brought 2 gallons, or 8/4 gallons. So, together, they brought ...

  7/4 + 8/4 = 15/4 gallons

Dividing that quantity evenly between them, each hiker gets ...

  (1/3)(15/4) = 5/4 gallons

This means James contributes ... (8/4 -5/4) = 3/4 gallon to Lou, while Karen contributes (7/4 -5/4) = 2/4 gallon to Lou.

If the $2 Lou contributed is divided in proportion to the water received, then for each quart Lou received, he has effectively paid

  $2/(5 quarts) = $0.40 per quart

Since James contributed 3 quarts, he should receive

  (3 quarts)($0.40/quart) = $1.20

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