To determine the rate at which Lúcia is using energy in calories per minute, we need to convert the given rate of 420 kilocalories per hour to calories per minute. Here are the detailed steps:
1. Understanding the Units:
- We have the energy rate given in kilocalories per hour: [tex]\( 420 \, \text{kcal} / \text{hr} \)[/tex].
- We want to convert this rate to calories per minute ([tex]\( \text{cal} / \text{min} \)[/tex]).
2. Converting Kilocalories to Calories:
- 1 kilocalorie is equivalent to 1000 calories.
- Therefore, [tex]\( 420 \, \text{kcal} \)[/tex] is equal to [tex]\( 420 \times 1000 \, \text{cal} \)[/tex].
[tex]\[
420 \, \text{kcal} = 420 \times 1000 \, \text{cal} = 420000 \, \text{cal}
\][/tex]
3. Converting Hours to Minutes:
- 1 hour is equivalent to 60 minutes.
4. Converting the Rate:
- We need to express the rate of 420000 calories per hour in terms of calories per minute.
- Since 1 hour = 60 minutes, the rate in calories per minute is found by dividing the total calories per hour by the number of minutes in an hour:
[tex]\[
\frac{420000 \, \text{cal}}{60 \, \text{min}} = 7000 \, \text{cal} / \text{min}
\][/tex]
Therefore, Lúcia is using energy at a rate of [tex]\( 7000 \, \text{cal} / \text{min} \)[/tex].
