Question

Leah walked 4/5 of a mile in 3/8 of an hour.

What was Leah’s walking speed in miles per hour?

Responses
A 12/40 mph






B 12/32 mph






C 1 13/15 mph






D 2 2/15 mph

Answer 1

To find Leah's walking speed in miles per hour, we need to divide the distance she walked by the time it took her to walk that distance.

Leah walked \( \frac{4}{5} \) of a mile in \( \frac{3}{8} \) of an hour.

Her walking speed \( S \) in miles per hour is given by:

\[
S = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{4}{5}}{\frac{3}{8}}
\]

To divide by a fraction, we multiply by its reciprocal:

\[
S = \frac{4}{5} \times \frac{8}{3}
\]

Now, we can multiply the fractions:

\[
S = \frac{4 \times 8}{5 \times 3} = \frac{32}{15}
\]

Now we can convert \( \frac{32}{15} \) into a mixed number:
- Divide 32 by 15. \( 32 \div 15 = 2 \) with a remainder of 2.
- Thus, we can write this as \( 2 \frac{2}{15} \).

Therefore, Leah’s walking speed is:

\[
\boxed{2 \frac{2}{15}} \text{ mph}
\]

The correct answer is option D: \( 2 \frac{2}{15} \) mph.