Sadie drove 13, one half13

2
1

miles in start fraction, 2, divided by, 3, end fraction
3
2

hours. On average, how fast did she drive, in miles per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.

1 answer

To find Sadie's average speed in miles per hour, we can use the formula for speed, which is:

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

Given that Sadie drove a distance of \(13 \frac{1}{2}\) miles, let's first convert this mixed number into an improper fraction:

\[ 13 \frac{1}{2} = \frac{26}{2} + \frac{1}{2} = \frac{27}{2} \text{ miles} \]

Her time of travel is given as \(\frac{2}{3}\) hours. Now we can plug these values into the speed formula:

\[ \text{Speed} = \frac{\frac{27}{2}}{\frac{2}{3}} \]

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

\[ \text{Speed} = \frac{27}{2} \times \frac{3}{2} = \frac{27 \times 3}{2 \times 2} = \frac{81}{4} \text{ miles per hour} \]

Next, we can express \(\frac{81}{4}\) as a mixed number:

\[ \frac{81}{4} = 20 \frac{1}{4} \]

Thus, Sadie's average speed is:

\[ \boxed{20 \frac{1}{4}} \text{ miles per hour} \]

We can also leave it in improper fraction form as \(\frac{81}{4}\), which is also an appropriate answer. So, in simplest form, her average speed is:

\[ \boxed{\frac{81}{4}} \text{ miles per hour} \]