# MAth

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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.
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 mi/h for 3 h in a week, how many calories do they burn? = Jogging 5 mi/h 740
2. If a person runs in place for 15 minutes, how many calories will be burned?
3. If a person cross-country skis for35minutes, how many calories will be burned?
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.)
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.
5. At what rate would a 120-pound person burn calories while bicycling at 12 mi/h?
6. At what rate would a 180-pound person burn calories while bicycling at 12 mi/h?
7. How many hours of jogging at 5 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.)

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

• MAth -

1. If a person jogs at a rate of 5 mi/h for 3 h in a week, how many calories do they burn? = Jogging 5 mi/h 740
Multiply 3 * 740.

2. If a person runs in place for 15 minutes, how many calories will be burned?
Since a person uses 650 calories per hour by running in place, she must use only 0.25 (1/4) of those calories in 15 minutes (1/4 of an hour).

3. If a person cross-country skis for35minutes, how many calories will be burned?
Set up a proportion:
700 / 1 = x / (35/60)

5. At what rate would a 120-pound person burn calories while bicycling at 12 mi/h?
Set up a proportion:
120/150 = x/410

• MAth -

1) If a person jogs at a rate of 5 1/2 mi/h for 3 1/2 h in a week, how many calories do they burn?
5.5 mi/h gives a calorie burn rate of 740 calories/hour.
If you jogged for 3.5 hours, you burned 740 * 3.5 = 2,590 calories/week.

2) If a person runs in place for 15 minutes, how many calories will be burned?
650 * (15/60) = 162.5 calories.

3) If a person cross-country skis for 35 minutes, how many calories will be burned?
700 * (35/60) = 408.3 calories

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.)
3500 / 750 = 4.666... = 4 hours and 40 minutes.

5) At what rate would a 120-pound person burn calories while bicycling at 12 mi/h?
410 * (120/150) = 328 calories/hour

6) At what rate would a 180-pound person burn calories while bicycling at 12 mi/h?
410 * (180/150) = 492 calories/hour

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.)
(3500 * 5) / ( (200/150) * 740) = 17.7364.. = 17 hours and about 44 minutes.

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