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Aidan ran (3)/(4) mile in a race. Bryan ran (2)/(5) of the distance that Aidan ran. What distance did Bryan run?

Aidan ran 34 \frac{3}{4} mile in a race. Bryan ran 25 \frac{2}{5} of the distance that Aidan ran. What distance did Bryan run?

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Full solution

Q. Aidan ran 34 \frac{3}{4} mile in a race. Bryan ran 25 \frac{2}{5} of the distance that Aidan ran. What distance did Bryan run?
  1. Calculate Aidan's distance: Aidan ran 34\frac{3}{4} mile. To find the distance Bryan ran, we need to calculate 25\frac{2}{5} of Aidan's distance.
  2. Multiply by 22/55: Multiply Aidan's distance by 25\frac{2}{5}: (34)×(25)\left(\frac{3}{4}\right) \times \left(\frac{2}{5}\right).
  3. Perform multiplication: Do the multiplication: (3×2)/(4×5)=6/20(3 \times 2) / (4 \times 5) = 6 / 20.
  4. Simplify fraction: Simplify the fraction 620\frac{6}{20} by dividing both numerator and denominator by their greatest common divisor, which is 22: 620=(6/2)(20/2)=310\frac{6}{20} = \frac{(6/2)}{(20/2)} = \frac{3}{10}.
  5. Find Bryan's distance: Bryan ran 310\frac{3}{10} of a mile.

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