Answer :
Final answer:
The athlete's total oxygen consumption after running 10.5 miles is calculated by converting their weight to kilograms, calculating their oxygen consumption rate per minute, determining the total running time in minutes, and multiplying these values. After all these steps, the final oxygen consumption of the athlete is found to be approximately 352.52 liters.
Explanation:
The subject of this question, which involves calculating the amount of oxygen consumed by an athlete based on their weight and speed, falls under the category of Mathematics and specifically rate calculations. It would typically be studied by high school students who are familiar with unit conversion and calculations involving proportions.
Let's begin by converting the weight of the athlete from pounds to kilograms, using the given conversion factor (1 kg = 2.2046 lb).
Weight in kilograms = Weight in lbs / 2.2046 = 157 lbs / 2.2046 = ~71.18 kg.
Now, we know that this athlete consumes 55.8 cm³ of oxygen per kilogram of body weight for every minute spent running. So for our 71.18 kg athlete, this means they consume:
Oxygen consumption in cm³ per minute = 55.8 cm³/kg/min * 71.18 kg = ~3969.94 cm³/min
Then, let's convert the distance that the athlete runs from miles to hours. Given that the athlete runs at a speed of 7.09 miles per hour, running 10.5 miles will take:
Time in hours = Distance / Speed = 10.5 miles / 7.09 mph = ~1.48 hr
Convert this time in hours to time in minutes (since we are calculating oxygen consumption per minute):
Time in minutes = Time in hours * 60 = 1.48 hr * 60 = ~88.8 min
Lastly, multiply the athlete's oxygen consumption per minute by the total number of minutes they run to get their total oxygen consumption, and convert from cm³ to liters (since 1 cm³ = 0.001 L):
Total Oxygen Consumption in Liters = Oxygen consumption rate * Time = 3969.94 cm³/min * 88.8 min * 0.001 L/cm³ = ~352.52 L
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