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 solve these problems, we need to use the information given in the table, which shows the number of calories burned per hour for different activities. We also need to know that in order to lose 1 pound, a person needs to burn off 3,500 calories more than they take in.
1. To find out how many calories a person burns by jogging at a rate of 5 1/2 mi/h for 3 1/2 h in a week, we need to multiply the calories burned per hour for jogging at 5 1/2 mi/h (740 cal/h) by the number of hours (3 1/2 h).
740 cal/h * 3 1/2 h = 2590 calories
Therefore, the person would burn 2590 calories.
2. To find out how many calories a person burns by running in place for 15 minutes, we need to convert the time to hours (15 minutes = 15/60 = 1/4 hour) and then multiply it by the calories burned per hour for running in place (650 cal/h).
(650 cal/h) * (1/4 h) = 162.5 calories
Therefore, the person would burn 162.5 calories.
3. To find out how many calories a person burns by cross-country skiing for 35 minutes, we need to convert the time to hours (35 minutes = 35/60 = 7/12 hour) and then multiply it by the calories burned per hour for cross-country skiing (700 cal/h).
(700 cal/h) * (7/12 h) ≈ 431.6 calories
Therefore, the person would burn approximately 431.6 calories.
4. To find out how many hours a person would have to jump rope in order to lose 1 pound, we need to divide the number of calories needed to lose 1 pound (3,500 calories) by the calories burned per hour for jumping rope (750 cal/h).
3,500 cal / 750 cal/h = 4.67 hours
Since we can't have a fraction of an hour, we can round it up to 5 hours. Therefore, the person would have to jump rope for 5 hours to lose 1 pound.
5. To calculate the rate at which a 120-pound person would burn calories while bicycling at 12 mi/h, we need to find the calories burned per hour for bicycling at 12 mi/h in the table (410 cal/h).
Since heavier people burn more calories, we can set up a proportion:
(150 lb) / (120 lb) = (410 cal/h) / x
Solving for x:
x = (120 lb * 410 cal/h) / 150 lb
x ≈ 328 cal/h
Therefore, a 120-pound person would burn approximately 328 calories per hour while bicycling at 12 mi/h.
6. Similarly, to calculate the rate at which a 180-pound person would burn calories while bicycling at 12 mi/h, we can set up the proportion:
(150 lb) / (180 lb) = (410 cal/h) / x
Solving for x:
x = (180 lb * 410 cal/h) / 150 lb
x ≈ 492 cal/h
Therefore, a 180-pound person would burn approximately 492 calories per hour while bicycling at 12 mi/h.
7. To find out how many hours of jogging at 5 1/2 mi/h would be needed for a 200-pound person to lose 5 pounds, we need to use the same principle. However, we need to adjust for the fact that losing 5 pounds requires burning off 3,500 calories * 5 = 17,500 calories.
So, we set up the proportion:
(150 lb) / (200 lb) = (740 cal/h) / x
Solving for x:
x = (200 lb * 740 cal/h) / 150 lb
x ≈ 986.7 cal/h
Now, we divide the total number of calories needed to lose 5 pounds (17,500 calories) by the calories burned per hour (986.7 cal/h):
17,500 cal / 986.7 cal/h ≈ 17.74 hours
Therefore, a 200-pound person would need to jog at 5 1/2 mi/h for approximately 17.74 hours to lose 5 pounds.