Suppose it takes John 40 minutes to run 5 miles. How long would it take him to run 7 kilometers?
The correct answer and explanation is:
Correct Answer: Approximately 35 minutes
To determine how long it would take John to run 7 kilometers, start by understanding his running speed and converting the distance from kilometers to miles.
Step 1: Calculate John’s speed in miles per minute
John runs 5 miles in 40 minutes. Speed=5 miles40 minutes=0.125 miles per minute\text{Speed} = \frac{5 \text{ miles}}{40 \text{ minutes}} = 0.125 \text{ miles per minute}
Step 2: Convert kilometers to miles
Use the conversion factor:
1 kilometer ≈ 0.621371 miles 7 kilometers×0.621371=4.349597 miles≈4.35 miles7 \text{ kilometers} \times 0.621371 = 4.349597 \text{ miles} \approx 4.35 \text{ miles}
Step 3: Calculate time to run 4.35 miles
Using his speed of 0.125 miles per minute: Time=4.35 miles0.125 miles/minute=34.8 minutes\text{Time} = \frac{4.35 \text{ miles}}{0.125 \text{ miles/minute}} = 34.8 \text{ minutes}
Rounding to the nearest whole number, John would take approximately 35 minutes to run 7 kilometers.
Explanation
This problem involves unit conversion and basic proportional reasoning. First, by dividing distance by time, John’s running speed is calculated. This rate is a key value because it allows for the time to be determined for any other distance.
Next, it is essential to convert 7 kilometers into miles since John’s speed was initially given in miles per minute. Multiplying by the conversion factor (1 km ≈ 0.621371 miles) gives the equivalent distance in miles.
Finally, the time required to run the new distance is found by dividing the total number of miles by the running speed. The result is then rounded to a reasonable level of precision. This method ensures that all calculations are consistent with the original units of measure.