Question

8 which speeds are equal to (\frac{1}{2}) mile per hour? mark all that apply.
a. (\frac{\frac{5}{6}\text{mi}}{\frac{5}{12}\text{h}})
(\bigcirc) b. (\frac{\frac{1}{4}\text{mi}}{\frac{1}{2}\text{h}})
(\bigcirc) c. (\frac{\frac{1}{10}\text{h}}{\frac{1}{5}\text{mi}})
(\bigcirc) d. (\frac{\frac{3}{8}\text{mi}}{\frac{3}{4}\text{h}})
(\bigcirc) e. (\frac{\frac{2}{3}\text{h}}{\frac{1}{3}\text{mi}})
(\bigcirc) f. (\frac{\frac{4}{5}\text{mi}}{\frac{4}{10}\text{h}})

Explanation:

Step1: Simplify each speed (mi/h)

To find speed, calculate $\frac{\text{distance}}{\text{time}}$ for each option:

Option A:

$$\frac{\frac{5}{6}\text{ mi}}{\frac{5}{12}\text{ h}} = \frac{5}{6} \times \frac{12}{5} = 2\text{ mi/h}$$

Option B:

$$\frac{\frac{1}{4}\text{ mi}}{\frac{1}{2}\text{ h}} = \frac{1}{4} \times \frac{2}{1} = \frac{1}{2}\text{ mi/h}$$

Option C:

$$\frac{\frac{1}{10}\text{ h}}{\frac{1}{5}\text{ mi}} = \frac{1}{10} \times \frac{5}{1} = \frac{1}{2}\text{ h/mi}$$
This is time per mile, reciprocal of speed: speed = $2\text{ mi/h}$

Option D:

$$\frac{\frac{3}{8}\text{ mi}}{\frac{3}{4}\text{ h}} = \frac{3}{8} \times \frac{4}{3} = \frac{1}{2}\text{ mi/h}$$

Option E:

$$\frac{\frac{2}{3}\text{ h}}{\frac{1}{3}\text{ mi}} = \frac{2}{3} \times \frac{3}{1} = 2\text{ h/mi}$$
Reciprocal speed = $\frac{1}{2}\text{ mi/h}$

Option F:

$$\frac{\frac{4}{5}\text{ mi}}{\frac{4}{10}\text{ h}} = \frac{4}{5} \times \frac{10}{4} = 2\text{ mi/h}$$

Step2: Match to $\frac{1}{2}$ mi/h

Identify options where speed equals $\frac{1}{2}$ mi/h.

Answer:

B. $\frac{\frac{1}{4}\text{ mi}}{\frac{1}{2}\text{ h}}$
D. $\frac{\frac{3}{8}\text{ mi}}{\frac{3}{4}\text{ h}}$
E. $\frac{\frac{2}{3}\text{ h}}{\frac{1}{3}\text{ mi}}$