Grace rides her horse 36 miles in 2 hours 15 minutes. what is the average speed in miles per hour?
The correct answer and explanation is:
To find the average speed, use the formula for speed, which is: Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
In this case, the total distance is 36 miles, and the total time is 2 hours 15 minutes. First, convert the time into hours for consistency. Since 15 minutes is a quarter of an hour, 15 minutes is: 1560=0.25 hours\frac{15}{60} = 0.25 \text{ hours}
Now, the total time in hours is: 2 hours+0.25 hours=2.25 hours2 \text{ hours} + 0.25 \text{ hours} = 2.25 \text{ hours}
Next, plug the total distance and total time into the formula for average speed: Average Speed=36 miles2.25 hours=16 miles per hour\text{Average Speed} = \frac{36 \text{ miles}}{2.25 \text{ hours}} = 16 \text{ miles per hour}
Thus, Grace’s average speed is 16 miles per hour.
Explanation:
To calculate the average speed, you need both the total distance and the total time. Speed is a measure of how fast something is moving, and it is commonly expressed as miles per hour (mph) for long distances in the United States. The key is to ensure that both the distance and time are in the correct units—miles for distance and hours for time.
First, you need to make sure the time is in hours. Converting minutes into a fraction of an hour helps simplify the calculation. After the conversion, use the average speed formula to determine the result. The outcome of 16 mph tells you that, on average, Grace travels 16 miles for every hour she rides. This method can be applied to any similar scenario where distance and time are given.