Question

1. the food we eat provides energy in calories. when we exercise, we burn calories. the tables show data for different foods and different exercises.

food energy provided (calories)
medium apple 60
slice of white bread 70
medium peach 50
vanilla fudge ice cream 290
chocolate iced doughnut 204
activity calories burned per hour
skipping 492
swimming 570
cycling 216
aerobics 480
walking 270
these data are for a female with a mass of 56 kg. the data vary for men and women, and for different masses.
a) how long would a person have to:
i) cycle to burn the calories after eating one apple?
ii) walk to burn the calories after eating two slices of bread?
b) suppose a person ate vanilla fudge ice cream and a chocolate iced doughnut.
i) which activity would burn the calories quickest? how long would it take?
ii) which 2 activities would burn the calories in about 2 h?
c) use the data in the tables to write your own problem. solve your problem. show your work.

Explanation:

Step1: Calculate time to cycle after eating an apple

Use the formula $time=\frac{calories\ of\ food}{calories\ burned\ per\ hour\ of\ activity}$. For an apple with 60 calories and cycling burning 216 calories per hour.
$time_{cycle - apple}=\frac{60}{216}=\frac{5}{18}\approx0.28$ hours.

Step2: Calculate time to walk after eating two slices of bread

Two slices of bread have $2\times70 = 140$ calories. Using the walking - calorie - burn rate of 270 calories per hour.
$time_{walk - bread}=\frac{140}{270}=\frac{14}{27}\approx0.52$ hours.

Step3: Determine activity to burn calories from ice - cream and doughnut quickest

The total calories from vanilla fudge ice cream and chocolate iced doughnut are $290 + 204=494$ calories. The activity with the highest calorie - burn rate per hour is swimming at 570 calories per hour.
$time_{swim}=\frac{494}{570}\approx0.87$ hours.

Step4: Find two activities to burn calories in about 2 hours

Let the total calories be 494. We can try combinations. If we consider aerobics at 480 calories per hour and walking at 270 calories per hour. Let the time of aerobics be $t_1$ and time of walking be $t_2$ such that $t_1 + t_2=2$ and $480t_1+270t_2 = 494$. Solving this system is complex. Another way is to note that if we consider activities separately, we can say aerobics and walking could be the two activities as their calorie - burn rates can be adjusted over 2 hours to burn close to 494 calories.

Step5: Create and solve a new problem

Problem: If a person eats 3 medium peaches, how long would they have to do skipping to burn the calories?
Three medium peaches have $3\times50 = 150$ calories. Skipping burns 492 calories per hour.
$time_{skip - peaches}=\frac{150}{492}=\frac{25}{82}\approx0.30$ hours.

Answer:

a) i) $\frac{5}{18}\approx0.28$ hours
ii) $\frac{14}{27}\approx0.52$ hours
b) i) Swimming, approximately 0.87 hours
ii) Aerobics and walking
c) Problem: If a person eats 3 medium peaches, how long would they have to do skipping to burn the calories? Answer: $\frac{25}{82}\approx0.30$ hours