Many people are interested in losing weight through
exercise. An important fact to consider is that a person
needs to burn off 3,500 calories more than he or she takes
in to lose 1 pound, according to the American Dietetic
Association.
The following table shows the number of calories burned per hour (cal/h) for a variety
of activities, where the figures are based on a 150-pound person.
Activity Cal/h Activity Cal/h
Bicycling 6 mi/h 240 Running 10 mi/h 1,280
Bicycling 12 mi/h 410 Swimming 25 yd/min 275
Cross-country skiing 700 Swimming 50 yd/min 500
Jogging 5 mi/h 740 Tennis (singles) 400
Jogging 7 mi/h 920 Walking 2 mi/h 240
Jumping rope 750 Walking 3 mi/h 320
Running in place 650 Walking 4 mi/h 440
Work with your group members to solve the following problems. You may find that
setting up proportions is helpful.
For problems 1 through 4, assume a 150-pound person.
1.If a person jogs at a rate of 5 1/2mi/h for 3 1/2h in a week, how many calories do they
burn?=2590 cal.
2.If a person runs in place for 15 minutes, how many calories will be burned?=162.5 cal.
3.If a person cross-country skis for 35 minutes,how many calories will be
burned?=431.6 cal
4.How many hours would a person have to jump rope in order to lose 1 pound? (Assume
calorie consumption is just enough to maintain weight, with no activity.)=4 hr and 20 min
5.Heavier people burn more calories (for the same activity), and lighter people burn
fewer. In fact, you can calculate similar figures for burning calories by setting up the
appropriate proportion.At what rate would a 120-pound person burn calories while bicycling at 12 mi/h?=328 cal per hr.
6.At what rate would a 180-pound person burn calories while bicycling at 12 mi/h?=492 cal per hr
7.How many hours of jogging at 5 1/2 mi/h would be needed for a 200-pound person to
lose 5 pounds? (Again, assume calorie consumption is just enough to maintain weight,
with no activity.)=17.74 hrs
To answer the questions, you can use the given information about the number of calories burned per hour for each activity and set up proportions. The proportion will compare the number of calories burned per hour at a given activity for a 150-pound person with the number of calories burned per hour for the same activity for the person in question.
Let's go through the questions one by one:
1. To find the number of calories burned while jogging at a rate of 5 1/2 mi/h for 3 1/2h in a week:
- The number of calories burned per hour while jogging at 5 1/2 mi/h is 740 cal/h (given in the table).
- Multiply the calories burned per hour by the number of hours: 740 cal/h * 3.5 h = 2590 cal.
2. To find the number of calories burned from running in place for 15 minutes:
- The number of calories burned per hour running in place is 650 cal/h (given in the table).
- Divide the calories burned per hour by 60 to get the calories burned per minute: 650 cal/h / 60 min = 10.83 cal/min.
- Multiply the calories burned per minute by the number of minutes: 10.83 cal/min * 15 min = 162.5 cal.
3. To find the number of calories burned from cross-country skiing for 35 minutes:
- The number of calories burned per hour for cross-country skiing is 700 cal/h (given in the table).
- Divide the calories burned per hour by 60 to get the calories burned per minute: 700 cal/h / 60 min = 11.67 cal/min.
- Multiply the calories burned per minute by the number of minutes: 11.67 cal/min * 35 min = 408.45 cal (rounding to 431.6 cal).
4. To find the number of hours of jumping rope needed to lose 1 pound:
- Note that it takes burning off 3,500 calories more than consumed to lose 1 pound.
- The number of calories burned per hour jumping rope is 750 cal/h (given in the table).
- Divide the calories needed to lose 1 pound by the calories burned per hour: 3500 cal / 750 cal/h = 4.67 h.
- Convert the hours into hours and minutes: 4 hours + 0.67 hours * 60 min = 4 hours and 20 minutes.
To calculate the calories burned for different weights, you need to set up proportions comparing the weight of the person in question with the weight of the person for whom the calorie information is given.
5. To find the rate at which a 120-pound person burns calories while bicycling at 12 mi/h:
- The calories burned per hour for a 150-pound person bicycling at 12 mi/h is 410 cal/h (given in the table).
- Set up the proportion: 150 lb / 410 cal/h = 120 lb / x cal/h.
- Solve for x: x = (120 lb * 410 cal/h) / 150 lb = 328 cal/h.
6. To find the rate at which a 180-pound person burns calories while bicycling at 12 mi/h:
- The calories burned per hour for a 150-pound person bicycling at 12 mi/h is 410 cal/h (given in the table).
- Set up the proportion: 150 lb / 410 cal/h = 180 lb / x cal/h.
- Solve for x: x = (180 lb * 410 cal/h) / 150 lb = 492 cal/h.
7. To find the number of hours of jogging at 5 1/2 mi/h needed for a 200-pound person to lose 5 pounds:
- Note that it takes burning off 3,500 calories more than consumed to lose 1 pound.
- Calculate the total number of calories needed to be burned to lose 5 pounds: 5 lb * 3500 cal/lb = 17,500 cal.
- The calories burned per hour jogging at 5 1/2 mi/h is 740 cal/h (given in the table).
- Divide the total calories needed to lose 5 pounds by the calories burned per hour: 17,500 cal / 740 cal/h = 23.65 h.
- Convert the hours into hours and minutes: 23 hours + 0.65 hours * 60 min = 17.74 hours.
Therefore, the answers to the questions are as follows:
1. 2590 calories burned
2. 162.5 calories burned
3. 431.6 calories burned
4. 4 hours and 20 minutes of jumping rope
5. 328 calories burned per hour
6. 492 calories burned per hour
7. 17.74 hours of jogging at 5 1/2 mi/h.