Please help me to resolve that sevent questions.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.
Chart:
Activity Cal/h
Bicycling 6 mi/h 240
Bicycling 12 mi/h 410
Cross-country skiing 700
Jogging 5 1/2 mi/h 740
Jogging 7 mi/h 920
Jumping rope 750
Running in place 650
Running 10 mi/h 1280
Swimming 25 yd/min 275
Swimming 50 yd/min 500
Tennis (single) 400
Walking 2 mi/h 240
Walking 3 mi/h 320
Walking 4 1/2 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 1/2 mi/h for 31/2 h in a week, how many calories do they
burn?

2. If a person runs in place for 15 minutes, how many calories will be burned?

3. Iersoncross-countryskis for35minutes,howmanycalories willbeburned?

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.)
1
2
1
2
1
2
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
1
2
1
2

Question 7 is 5 1/2 not 5

20

To solve these problems, we can use the formula provided by the American Dietetic Association, which states that a person needs to burn off 3,500 calories more than they consume to lose 1 pound. We also have a table that shows the number of calories burned per hour for various activities based on a 150-pound person. Let's go through each problem step by step.

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?

To find the number of calories burned, we can multiply the number of hours by the calories burned per hour for jogging at 5 1/2 mi/h.

3 1/2 hours jogging at 5 1/2 mi/h = (3.5) * (740 cal/h) = 2590 calories burned.

So, the person burns 2590 calories.

2. If a person runs in place for 15 minutes, how many calories will be burned?

First, we need to convert 15 minutes to hours. There are 60 minutes in an hour, so 15 minutes is equal to 15/60 = 1/4 hour.

Next, we multiply the calories burned per hour for running in place by the number of hours.

(1/4) hour running in place = (1/4) * (650 cal/h) = 162.5 calories burned.

So, the person burns 162.5 calories.

3. If a person cross-country skis for 35 minutes, how many calories will be burned?

Similar to problem 2, we need to convert 35 minutes to hours.

35 minutes = 35/60 = 7/12 hour.

Then, we multiply the calories burned per hour for cross-country skiing by the number of hours.

(7/12) hour cross-country skiing = (7/12) * (700 cal/h) = 408.33 calories burned.

So, the person burns approximately 408.33 calories.

4. How many hours would a person have to jump rope in order to lose 1 pound?

Since jumping rope is not listed in the table, we can assume that the person burns the same number of calories as they do when running in place, which is 650 cal/h.

To lose 1 pound, they need to burn off 3,500 calories more than they consume. Therefore, the person needs to jump rope for 3,500/650 = 5.38 hours.

So, the person would need to jump rope for approximately 5.38 hours to lose 1 pound.

Now let's move on to the next set of problems.

5. At what rate would a 120-pound person burn calories while bicycling at 12 mi/h?

Since the table shows calories burned based on a 150-pound person, we need to calculate the rate for a 120-pound person. We can set up a proportion to solve this.

Calories burned per hour for a 150-pound person = 410 cal/h.
Calories burned per hour for a 120-pound person = x cal/h.

Using the proportion:
(150 lbs)/(120 lbs) = (410 cal/h)/x cal/h.

Simplifying the proportion:
1.25 = 410/x.

Now, we can solve for x by dividing both sides of the equation by 1.25:
x = 410/1.25 = 328 cal/h.

So, a 120-pound person would burn calories at a rate of 328 cal/h while bicycling at 12 mi/h.

6. At what rate would a 180-pound person burn calories while bicycling at 12 mi/h?

Using a similar approach as in problem 5, we can set up a proportion to find the rate at which a 180-pound person would burn calories.

Calories burned per hour for a 150-pound person = 410 cal/h.
Calories burned per hour for a 180-pound person = x cal/h.

Using the proportion:
(150 lbs)/(180 lbs) = (410 cal/h)/x cal/h.

Simplifying the proportion:
0.8333 = 410/x.

Solving for x:
x = 410/0.8333 = 492.05 cal/h.

So, a 180-pound person would burn calories at a rate of approximately 492.05 cal/h while bicycling at 12 mi/h.

7. How many hours of jogging at 5 1/2 mi/h would be needed for a 200-pound person to lose 5 pounds?

Similar to problem 1, we can calculate the number of calories burned by multiplying the number of hours by the calories burned per hour for jogging at 5 1/2 mi/h.

Since the person wants to lose 5 pounds, they need to burn off 5 * 3,500 = 17,500 calories more than they consume.

Let's assume the calorie consumption is just enough to maintain weight, so it doesn't contribute to losing or gaining weight.

To find the number of hours needed, we use the formula:
Number of hours = (Calories needed to burn) / (Calories burned per hour).

Calories needed to burn = 17,500 calories.
Calories burned per hour for jogging at 5 1/2 mi/h = 740 cal/h.

Number of hours = 17,500 cal / 740 cal/h = 23.65 hours.

So, a 200-pound person would need to jog for approximately 23.65 hours at 5 1/2 mi/h to lose 5 pounds.