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Ruby went on a walk that was [tex]\frac{10}{3}[/tex] miles long. She stopped to have lunch when she had walked [tex]\frac{12}{25}[/tex] of the way.

How far, in miles, did Ruby walk before lunch? Give your answer as a fraction in its simplest form.

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GinnyAnswer
To determine the distance Ruby walked before lunch, we can follow these steps:

1. Identify the total distance of Ruby's walk:
Ruby walked a total distance of \(\frac{10}{3}\) miles.

2. Identify the fraction of the walk completed before lunch:
Ruby walked \(\frac{12}{25}\) of the total distance before stopping for lunch.

3. Calculate the distance walked before lunch:
To find the distance Ruby walked before lunch, we need to multiply the total distance by the fraction of the way she walked.

Given:
[tex]\[ \text{Total distance} = \frac{10}{3} \text{ miles} \][/tex]
[tex]\[ \text{Fraction walked before lunch} = \frac{12}{25} \][/tex]

Therefore, the distance walked before lunch is:
[tex]\[ \text{Distance before lunch} = \left( \frac{10}{3} \right) \times \left( \frac{12}{25} \right) \][/tex]

4. Simplify the calculation:
Multiply the numerators together and the denominators together:
[tex]\[ \text{Distance before lunch} = \frac{10 \times 12}{3 \times 25} = \frac{120}{75} \][/tex]

5. Simplify the fraction:
The fraction \(\frac{120}{75}\) can be simplified by finding the greatest common divisor (GCD) of 120 and 75, which is 15. Simplify by dividing both the numerator and the denominator by 15:
[tex]\[ \frac{120 \div 15}{75 \div 15} = \frac{8}{5} \][/tex]

Thus, Ruby walked [tex]\(\frac{8}{5}\)[/tex] miles before lunch.
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