An athlete can run 6 miles in 51 minutes. At this rate, how many miles could the athlete run in 90 minutes?
A.
15 miles
B.
11.5 miles
C.
45 miles
D.
10.6 miles
The correct answer and Explanation is :
To determine how many miles an athlete can run in 90 minutes given their running rate of 6 miles in 51 minutes, follow these steps:
- Calculate the athlete’s running rate:
The athlete runs 6 miles in 51 minutes. To find the rate in miles per minute, divide the distance by the time:
[
\text{Rate} = \frac{6 \text{ miles}}{51 \text{ minutes}} \approx 0.1176 \text{ miles per minute}
] - Calculate the distance the athlete can run in 90 minutes:
Use the rate calculated in the previous step and multiply it by the total time (90 minutes) to find out how many miles the athlete can cover:
[
\text{Distance} = \text{Rate} \times \text{Time}
]
[
\text{Distance} = 0.1176 \text{ miles per minute} \times 90 \text{ minutes} \approx 10.64 \text{ miles}
] - Round to the nearest option:
The calculated distance of approximately 10.64 miles is closest to 10.6 miles.
Therefore, the correct answer is D. 10.6 miles.
Explanation
To solve this problem, the key is to determine the athlete’s rate of running per minute and then use this rate to estimate the distance covered in a different amount of time. By dividing the total distance (6 miles) by the time taken (51 minutes), you get a rate of 0.1176 miles per minute. Multiplying this rate by the desired time (90 minutes) gives you the total distance the athlete can run in that time frame.
This method involves basic unit conversions and proportional reasoning. Ensuring that units are consistent and accurately performing the calculations are crucial steps to finding the correct answer.