Unit Rates for Ratios with Fractions, Part 2 - Quiz - Level G Madison and Declan are training for a lifeguard test. Madison swims \( \frac{2}{5} \) mile in \( \frac{3}{8} \) hour. Declan swi \( \frac{7}{10} \) mile in \( \frac{1}{5} \) hour. Who swims faster?

To determine who swims faster, we need to calculate the unit rate (miles per hour) for both Madison and Declan. **For Madison:** - Distance: \( \frac{2}{5} \) mile - Time: \( \frac{3}{8} \) hour To find the unit rate, we divide the distance by the time: \[ \text{Unit rate for Madison} = \frac{\frac{2}{5}}{\frac{3}{8}} = \frac{2}{5} \times \frac{8}{3} = \frac{2 \times 8}{5 \times 3} = \frac{16}{15} \text{ miles per hour} \] **For Declan:** - Distance: \( \frac{7}{10} \) mile - Time: \( \frac{1}{5} \) hour Again, we divide the distance by the time: \[ \text{Unit rate for Declan} = \frac{\frac{7}{10}}{\frac{1}{5}} = \frac{7}{10} \times \frac{5}{1} = \frac{7 \times 5}{10 \times 1} = \frac{35}{10} = \frac{7}{2} = 3.5 \text{ miles per hour} \] Now we compare the two unit rates: - Madison: \( \frac{16}{15} \) miles per hour, which is approximately \( 1.07 \) miles per hour. - Declan: \( 3.5 \) miles per hour. Since \( 3.5 \) miles per hour is greater than \( 1.07 \) miles per hour, we conclude that: **Declan swims faster than Madison.**