Question

1. compare and contrast the rates \\(\frac{4}{5}\\) mile in 8 minutes and 4 minutes to travel \\(\frac{2}{5}\\) mile.

Explanation:

Step1: Calculate first rate

Rate is distance divided by time. For the first rate, distance is $\frac{4}{5}$ mile and time is 8 minutes. So rate $r_1 = \frac{\frac{4}{5}}{8}$. Simplify this: $\frac{4}{5} \div 8 = \frac{4}{5} \times \frac{1}{8} = \frac{4}{40} = \frac{1}{10}$ miles per minute.

Step2: Calculate second rate

For the second rate, distance is $\frac{2}{5}$ mile and time is 4 minutes. Rate $r_2 = \frac{\frac{2}{5}}{4}$. Simplify: $\frac{2}{5} \div 4 = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$ miles per minute.

Step3: Compare the rates

Both rates simplify to $\frac{1}{10}$ miles per minute, so they are equal.

Answer:

The two rates are equal, both being $\frac{1}{10}$ miles per minute.