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?

To solve this problem, let's go through the steps systematically:

1. **Total water collected**: Jeanette collects \( 42 \frac{1}{2} \) gallons of water. In improper fraction form:

   \[
   42 \frac{1}{2} = \frac{85}{2} \text{ gallons}
   \]

2. **Water used for watering plants**: Jeanette uses \( 1 \frac{1}{4} \) gallons for her plants. In improper fraction form:

   \[
   1 \frac{1}{4} = \frac{5}{4} \text{ gallons}
   \]

3. **Remaining water after watering plants**: Subtract the water used for plants from the total collected water:

   \[
   \text{Remaining water} = \frac{85}{2} - \frac{5}{4}
   \]

   To perform the subtraction, find a common denominator (which is 4):

   \[
   \frac{85}{2} = \frac{85 \times 2}{2 \times 2} = \frac{170}{4}
   \]

   Now, subtract:

   \[
   \frac{170}{4} - \frac{5}{4} = \frac{170 - 5}{4} = \frac{165}{4} \text{ gallons}
   \]

4. **Water used for laundry**: Jeanette uses \(\frac{1}{2}\) of the remaining water to wash laundry:

   \[
   \text{Water used for laundry} = \frac{1}{2} \times \frac{165}{4} = \frac{165}{8} \text{ gallons}
   \]

5. **Simplify \(\frac{165}{8}\) to a mixed number**:

   Divide 165 by 8:

   \[
   165 \div 8 = 20 \text{ R } 5
   \]

   So, 

   \[
   \frac{165}{8} = 20 \frac{5}{8} \text{ gallons}
   \]

Jeanette uses \( 20 \frac{5}{8} \) gallons of water to wash her laundry.

Would you like more details or have any questions?

Here are some related questions:

1. How much water is left after Jeanette washes her laundry?
2. If Jeanette wants to collect the same amount of water next time, how many barrels would she need if each can hold 10 gallons?
3. How much water would Jeanette use if she washed two loads of laundry with the same amount?
4. What is the fraction of water used for all activities out of the total collected?
5. How many times can Jeanette water her plants with the collected water?

**Tip**: Always convert mixed numbers to improper fractions when performing arithmetic operations for easier calculations!

Discover how many gallons of water Jeanette uses to wash laundry in this math problem solution. Learn about fractions and subtraction as Jeanette manages collected rainwater for various tasks. Suitable for Grades 4-6 students.

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