Question

yuki ran 2 3/4 miles in 2/5 hour. how fast did yuki tun in a miles per hour

Answer 1

To find out how fast Yuki ran in miles per hour, we can use the formula for speed:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

First, let's convert the distance Yuki ran, which is \(2 \frac{3}{4}\) miles, to an improper fraction:

\[
2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \text{ miles}
\]

Yuki ran this distance in \( \frac{2}{5} \) hour.

Now we can calculate the speed:

\[
\text{Speed} = \frac{\frac{11}{4} \text{ miles}}{\frac{2}{5} \text{ hour}}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\text{Speed} = \frac{11}{4} \times \frac{5}{2}
\]

Now, we can perform the multiplication:

\[
\text{Speed} = \frac{11 \times 5}{4 \times 2} = \frac{55}{8} \text{ miles per hour}
\]

Finally, we can express \( \frac{55}{8} \) as a mixed number if desired:

\[
\frac{55}{8} = 6 \frac{7}{8} \text{ miles per hour}
\]

Therefore, Yuki ran at a speed of:

\[
\frac{55}{8} \text{ miles per hour} \quad \text{or} \quad 6 \frac{7}{8} \text{ miles per hour}.
\]