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QuestionLúcia uses energy at 420 kcal/h. Find her energy use rate in calories/min (calmin)\left(\frac{\mathrm{cal}}{\mathrm{min}}\right).

Studdy Solution

STEP 1

Assumptions1. Lúcia is using energy at a rate of420 kilocalories (kcal) per hour (h) ice skating. . We need to convert this rate to calories per minute. 3.1 kilocalorie (kcal) is equivalent to1000 calories (cal). 4.1 hour is equivalent to60 minutes.

STEP 2

First, we need to convert the energy usage from kilocalories to calories. We can do this by multiplying the energy usage in kilocalories by1000.
Energy usage in calories=Energy usage in kilocaloriestimes1000Energy\, usage\, in\, calories = Energy\, usage\, in\, kilocalories \\times1000

STEP 3

Now, plug in the given value for the energy usage in kilocalories to calculate the energy usage in calories.
Energy usage in calories=420 kcaltimes1000Energy\, usage\, in\, calories =420\, kcal \\times1000

STEP 4

Calculate the energy usage in calories.
Energy usage in calories=420,000 calEnergy\, usage\, in\, calories =420,000\, cal

STEP 5

Next, we need to convert the time from hours to minutes. We can do this by multiplying the time in hours by60.
Time in minutes=Time in hourstimes60Time\, in\, minutes = Time\, in\, hours \\times60

STEP 6

Now, plug in the given value for the time in hours to calculate the time in minutes.
Time in minutes=1 htimes60Time\, in\, minutes =1\, h \\times60

STEP 7

Calculate the time in minutes.
Time in minutes=60 minTime\, in\, minutes =60\, min

STEP 8

Now that we have the energy usage in calories and the time in minutes, we can find the rate of energy usage in calories per minute. This can be done by dividing the energy usage in calories by the time in minutes.
Rate of energy usage=Energy usage in caloriesTime in minutesRate\, of\, energy\, usage = \frac{Energy\, usage\, in\, calories}{Time\, in\, minutes}

STEP 9

Plug in the values for the energy usage in calories and the time in minutes to calculate the rate of energy usage.
Rate of energy usage=420,000 cal60 minRate\, of\, energy\, usage = \frac{420,000\, cal}{60\, min}

STEP 10

Calculate the rate of energy usage in calories per minute.
Rate of energy usage=420,000 cal60 min=7,000 calminRate\, of\, energy\, usage = \frac{420,000\, cal}{60\, min} =7,000\, \frac{cal}{min}úcia is using energy at a rate of7,000 calories per minute.

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