Idil drove 12 miles in $\frac{1}{5}$ of an hour. On average, how fast did she drive, in miles per hour?

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msereyko msereyko

01-11-2026
Mathematics

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Idil drove 12 miles in $\frac{1}{5}$ of an hour. On average, how fast did she drive, in miles per hour?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T20:22:14-05:00

Identify the distance traveled ($12$ miles) and the time taken ($\frac{1}{5}$ hour).
Apply the formula for average speed: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.
Calculate the result: $\frac{12}{1/5} = 12 \times 5 = 60$.
Conclude that the average speed is $\boxed{60}$ miles per hour.

Explanation

Analyzing the Problem

The problem asks for the average speed of a car given the distance traveled and the time it took. We are given:

Distance traveled: $12$ miles.
Time taken: $\frac{1}{5}$ of an hour.

The average speed is defined as the ratio of the total distance traveled to the total time taken. The formula is:
\[\text{Speed} = \frac{\text{Distance}}{\text{Time}}\]
We want to express this speed in miles per hour, which is the distance traveled in one full hour.

Calculating the Speed

To find the speed, we substitute the given values into the formula:
\[\text{Speed} = \frac{12 \text{ miles}}{\frac{1}{5} \text{ hour}}\]
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of $\frac{1}{5}$ is $\frac{5}{1} = 5$.
Thus, the calculation becomes:
\[\text{Speed} = 12 \times 5 = 60\]
This means the car travels $60$ miles in $1$ hour. So, the speed is $60$ miles per hour.

Conceptualizing and Concluding

We can visualize this using a double number line. If we place "Time" on one axis and "Distance" on the other:

At $\frac{1}{5}$ hours, the distance is $12$ miles.
To reach $1$ hour (which is $5 \times \frac{1}{5}$ hours), we multiply the time by $5$.
To maintain the same speed, we must also multiply the distance by $5$:

\[12 \times 5 = 60 \text{ miles}\]
Therefore, in $1$ hour, the car travels $60$ miles, confirming that the average speed is $60$ miles per hour.
The final answer is $\boxed{60}$.

Examples

Average speed is a vital concept for planning travel and logistics. For example, if you are planning a road trip and know that your car covers a certain distance in a fraction of an hour, you can calculate your average speed to estimate your total arrival time. If you know you need to travel $300$ miles and your average speed is $60$ miles per hour, you can easily determine that it will take you $300 \div 60 = 5$ hours to reach your destination. Understanding this relationship helps in managing time effectively in everyday life.