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During a rain shower, Jeanette collects 42 1/2 gallons of water in a rain barrel outside her home. She uses 1 1/4 gallons to water plants inside her house. Then, she uses 1/2 of the remaining water to wash a load of dirty laundry. How many gallons of water does Jeanette use to wash her laundry?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.