Write the ratio or rate in simplest form.Write 781 mi in 14.2 h as a rate in simplest form.

1. Break Down the Problem

We need to express the distance of 781 miles over 14.2 hours as a rate. This can be done by dividing the distance by the time.

2. Relevant Concepts

The formula to find the rate $r$ is given as: $r = \frac{\text{distance}}{\text{time}}$

3. Analysis and Detail

Let's perform the calculations:

• Distance = 781 miles
• Time = 14.2 hours

Calculating the rate: $r = \frac{781 \text{ miles}}{14.2 \text{ hours}} \approx 55.0 \text{ miles per hour}$ Next, we check if this fraction can be simplified. We round the decimals for practical use, but since we're already in decimal form, we'll maintain it succinctly.

4. Verify and Summarize

To verify, multiplying the rate by the time should give us back the distance: $55.0 \text{ miles per hour} \times 14.2 \text{ hours} \approx 781 \text{ miles}$

Final Answer

The rate in simplest form is approximately $55.0$ miles per hour.