A runner wants to run 10.9km. ?
They know their running pace is 7.7 ?miles per hour. How many minutes must they run?
The correct answer and explanation is :
To determine how many minutes a runner must run to complete 10.9 kilometers at a pace of 7.7 miles per hour, we can break this problem into a series of steps.
Step 1: Convert kilometers to miles
Since the runner’s pace is given in miles per hour, we first need to convert the distance from kilometers to miles. We know that:
1 kilometer = 0.621371 miles
So, to convert 10.9 kilometers to miles:
[
10.9 \text{ km} \times 0.621371 = 6.771 \text{ miles}
]
Step 2: Calculate the time in hours
Next, we can use the formula:
[
\text{Time (in hours)} = \frac{\text{Distance (in miles)}}{\text{Speed (in miles per hour)}}
]
Substituting the values:
[
\text{Time} = \frac{6.771 \text{ miles}}{7.7 \text{ miles per hour}} = 0.880 \text{ hours}
]
Step 3: Convert hours to minutes
Since we are asked to find the time in minutes, we now convert hours to minutes. There are 60 minutes in an hour, so:
[
0.880 \text{ hours} \times 60 = 52.8 \text{ minutes}
]
Thus, the runner must run for approximately 52.8 minutes to cover the distance of 10.9 kilometers.
Explanation:
We began by converting the distance to miles because the runner’s pace was provided in miles per hour. After calculating the time in hours, we converted it to minutes to provide the final answer.
This process shows how distance, speed, and time are interconnected. When converting between units (in this case, kilometers to miles), we use a conversion factor to ensure the calculation is consistent with the units of the runner’s pace. By following these steps, we can determine how long it will take the runner to complete their run.