Question

tanya is training a turtle for a turtle race. for every \\(\frac{2}{3}\\) of an hour that the turtle is crawling, he can travel \\(\frac{1}{8}\\) of a mile. at what unit rate is the turtle crawling?\
\\(\bigcirc\\) a. \\(\frac{19}{24}\\) of a mile per hour\
\\(\bigcirc\\) b. 12 miles per hour\
\\(\bigcirc\\) c. \\(\frac{3}{16}\\) of a mile per hour\
\\(\bigcirc\\) d. \\(\frac{1}{12}\\) of a mile per hour

Explanation:

Step1: Recall the formula for unit rate (speed)

The formula for speed is \( \text{speed} = \frac{\text{distance}}{\text{time}} \). Here, the distance is \( \frac{1}{8} \) mile and the time is \( \frac{2}{3} \) hour.

Step2: Substitute the values into the formula

We need to calculate \( \frac{\frac{1}{8}}{\frac{2}{3}} \). Dividing by a fraction is the same as multiplying by its reciprocal, so this becomes \( \frac{1}{8} \times \frac{3}{2} \).

Step3: Multiply the fractions

Multiplying the numerators: \( 1\times3 = 3 \), and multiplying the denominators: \( 8\times2 = 16 \). So the result is \( \frac{3}{16} \) mile per hour.

Answer:

C. \( \frac{3}{16} \) of a mile per hour