Problem Set Solutions

1. Answer: 18.7 ml-min-l-kg-1

Solution:
VO, = 3.5 + 2.68(3.0) + 0.48(3.0)(5) = 3.5 + 8.04 + 7.2 = 18.74
2. Answer: 235 kcal
Solution:
V02 = 3.5 + 2.68(2.5) + 0.48(2.5)(6)
= 3.5 + 6.7 + 7.2
= 17.4 ml-min-l-kg-I
Convert to L-min-1: (1 7.4 x 90 kg)/l 000 1.566
Convert to kcal: 1.566 x 5 kcal-L-1 x 30 min 235
3. Answer: 6.4 METs
Solution:
V02 = 3.5 + 2.68(3.7) + 0.48(3.7)(5)
= 3.5 + 9.916 + 8.88
= 22.296 ml-min-'.kg-1
METs = 22.296/3.5 = 6.4




4. Answer: 19.1 ml-min-'.kg-1

Solution:
V02 = 3.5 + 2.68(2.8) + 0.48(2.8)(6) = 3.5 + 7.504 + 8.064 = 19.068
5. Answer: 4.0 METs
Solution:

V02 = 3.5 + 2.68(3.9) + 0.40(3.9)(0) = 3.5 + 10.452 + 0
= 13.952 ml-min-l-kg-1
Convert to METS: 13.952/3.5 = 3.986 6. Answer: 20%
Solution:
8.0 METs X 3.5 = 28 ml-min-l-kg-1
28 3.5 + 2.68(2.0) + 0.48(2.0)(%grade)
28 3.5 + 5.36 + 0.96(%grade)

19.4 = 0.96(%grade)
19.14/0.96 = %grade
19.9 = %grade
7. Answer: 2.9 mph

Solution:

5.2 METs x 3.5 = 18.2 ml-min-'.kg-1

18.2 = 3.5 + 2.68(speed) + 0.48(speed)(5)

18.2 = 3.5 + 2.68(speed) + 2.4(speed)

14.7 = (2.68 + 2.4)(speed)

14.7 = 5.08(speed)
14.7/5.08 = speed
2.89 = speed
8. Answer: 72 weeks

Solution:
V02 = 3.5 + 2.68(3) + 0.48(3)(3) = 3.5 + 8.04 + 4.32 = 15.86
Convert to L-min-1: (1 5.86 x 68 kg)/l 000 1.08 Convert to kcal-min-1: 1.08 L-min-I x 5 kcal-L-1 = 5.4 kcal-min-1 5.4 x 30 min x 3 times per week = 486 kcal each week 1 lb fat = 3500 kcal


1 0 lb fat = 35,000 kcal

35,000 kcal/486 kcal per week = 72 weeks

9. Answer: 126 liters

Solution:
V02 = 3.5 + 2.68(3.7) + 0.48(3.7)(10) = 3.5 + 9.916 + 17.76 = 31.2 ml-min-l-kg-I
Convert to L-min-1: (31.1 x 68)/1000 = 2.1 L-min-1
2.1 L-min-I x 60 minutes = 126
1 0. Answer: 4.0 mph
Solution:

V02max in ml-min-'.kg-I = (2.4 x 1000)/48 = 50
75% of 50 = 0.75 x 50 = 37.5 ml-min-l-kg-1
37.5 = 3.5 + 2.68(speed) + 0.48(speed)(12)

34 = 2.68(speed) + 5.76(speed)

34 = 8.44(speed)
34/8.44 = speed
4.028 = speed
1 1. Answer: 4.1 L-min-1

Solution:

V02 = 3.5 + 5.36(7) + 0.24(7)(3)

= 3.5 + 37.52 + 5.04

= 46.06 ml-min-l-kg-l

Convert to Limin-1: (46.06 x 90 kg)/1000 4.1
12. Answer: 14.3 METs
Solution:
V02 = 3.5 + 5.36(6) + 0.24(6)(1 0)
= 3.5 + 32.16 + 14.4
= 50.06 ml-min-l-kg-1
Convert to METS: 50.06/3.5 = 14.3
13. Answer: 51.7 ml-min-l-kg-1
Solution:
V02 = 3.5 + 5.36(9) + 0.48(9)(0)
= 3.5 + 48.24 + 0
= 51.74
14. Answer: 14.3 ME-Fs

Solution:

V02 3.5 + 5.36(5.2) + 0.24(5.2)(15)




= 3.5 + 27.872 + 18.72

= 50.09 ml-min-l-kg-l

Convert to METS: 50.09/3.5 = 14.3
15. Answer: 15 minutes

Solution:

V02 = 3.5 + 5.36(9) + 0.48(9)(0)

= 3.5 + 48.24 + 0

= 51.74 ml-min-l-kg-l

0.5 lb of fat = 3500/2 1750 kcal
1750/4 days per week 437.5 kcal per exercise session Convert V02 to L-min-1: (51.74 x 113 kg)/1000 = 5.8 Convert to kcal-min-1: 5.8 x 5 kcal-L-1 = 29.2 kcal-min-1 Time needed is: 437.5/29.2 = 14.9 minutes
16. Answer: 6.1 % grade
Solution:
80% of 1 1 METs is 8.8 METs
V02 8.8 x 3.5 = 30.8 ml-min-l-kg-1
30.8 3.5 + 5.36(4) + 0.24(4)(%grade)
30.8 3.5 + 21.44 + 0.96(%grade)
30.8 24.94 + 0.96 (%grade)
5.86 0.96(%grade)
5.86/0.96 = %grade
6.1 = %grade
17. Answer: 20.7 kcal-min-1
Solution:
V02 = 3.5 + 5.36(10) + 0.24(10)(5)
= 3.5 + 53.6 + 12.0
= 69.1 ml-min-'.kg-1

Convert to L-min-1: (69.1 x 60 kg)/1000 4.146 L-min-1 Convert to kcal-min-1: 4.146 x 5 kcal-L-1 20.73
18. Answer: 57 ml-min-l-kg-1

Solution:

Convert seconds to minutes: 18/60 = 0.30

Therefore, 30:18 seconds = 30.30 minutes

Convert minutes to hours: 30.30/60 = 0.505 hours

Speed = 5/0.505 = 9.9 mph so

V02 = 3.5 + 5.36(9.9) + 0.48(9.9)(0)

= 3.5 + 53.064 + 0

= 56.564

PF





19. Answer: Slow from 9.9 to 6.5 mph
Solution:
57 = 3.5 + 5.36(speed) + 0.48(speed)(6)
57 = 3.5 + 5.36(speed) + 2.88(speed)
57 = 3.5 + 8.24(speed)

53.5 = 8.24(speed)
53.5/8.24 = speed
6.49 = speed
20. Answer: 8.8% grade
Solution:
85% of 70 ml-min-'.kg-1 = 59.5 ml-min-l.kg-l
59.5 = 3.5 + 5.36(7.5) + 0.24(7.5)(%grade)

59.5 = 3.5 + 40.2 + 1.8(%grade)

15.8 = 1.8(%grade)
15.8/1.8 = %grade
8.777 = %grade
21. Answer: 36.8 ml-min-l-kg-1
Solution:
V02 = 3.5 + 2(1500)/90
= 3.5 + 33.33
= 36.83
22. Answer: 619 kcal

Solution:

V02 = 3.5 + 2(900)/75

= 3.5 + 24

= 27.5
Convert to L-min-1: (27.5 x 75 kg)/75 2.0625
Convert to kcal: 2.0625 x 5 kcal-min-1 10.3125
10.3125 x 60 minutes = 618.75
23. Answer: 37.8 ml-min-'.kg-1
Solution:
200 watts x 6 = 1200 kg-m-min-1
V02 = 3.5 _+ 2(1200)/70
= 3.5 + 34.29
= 37.79
24. Answer: 441 kg.m.min-1
Solution:
6.0 kcal-min-1/5 kcal-L-1 1.2 L-min-I
Convert V02 to ml-min-'.kg-l: (1.2 x 1000)/91 kg = 13.2
13.2 = 3.5 + 2(workload)/91
9.7 = 2(workload)91
9.7/2 = workload/91
4.85 x 91 = workload
441.35 = workload
25. Answer: 3.5 kg
Solution:
5.0 L-min-1 x 0.75 = 3.75 L-min-1
Convert V02 to ml-min-' kg-': (3.75 x 1 000)/l 1 0 kg 34.1

34.1 = 3.5 + 2(workload)/ 1 1 0

30.6 = 2(workload)/l 1 0
30.6/2 = workload/ 1 1 0 1 5.3 = workload/ 1 1 0 15.3 x 1 1 0 = workload 1683 = workload
Resistance setting:
1683 = (resistance setting)(80)(6) 1683 = (resistance setting)(480)
1683/480 = resistance setting
3.506 = resistance setting
26. Answer: 5.6 kg

Solution:

12 METs x 3.5 = 42 ml-min-l-kg-1 42 = 3.5 + 2(workload)/70
38.5 = 2(workload)/70
38.5/2 workload/70
19.25 workload/70
19.25 x 70 = workload

1347.5 kg.m-min-1 = workload
Resistance setting:
1347.5 = (resistance setting)(3)(80)

1347.5 = (resistance setting)(240)
1347.5/240 = resistance setting
5.614 = resistance setting
27. Answer: 30.2 ml-min-l-kg-1

Solution:

V02 = 3.5 + 3(800)/90




= 3.5 + 26.7

= 30.2
28. Answer: 1.2 L-min-I
Solution:
50 wafts X 6 = 300 kg-m-min-1
V02 = 3.5 + 3(300)/90
= 3.5 + 10
= 13.5 ml-min-l-kg-1
Convert to L-min-1: (13.5 x 90 kg)/looo 1.215
29. Answer: 7.1 ml-min-'.kg-1
Solution:
Workload = (0.5 kg)(2.4 m-rev-1)(50) 60 kg-m-min-I V02 = 3.5 + 3(60)/50
= 3.5 + 3.6
= 7.1
30. Answer: 5.2 hours
Solution:
V02 = 3.5 + 2(1000)/70
= 3.5 + 28.6
= 32.1 ml-min-'.kg-1
Convert to L-min-1: (32.1 x 70)/1000 2.247 L-min-1 2.247 x 5 kcal-L-1 = 11.2 kcal-min-1 3500 kcal/l 1.2 = 312.5 minutes 312.5/60 = 5.2
31. Answer: 21.6 ml-min-l-kg-1
Solution:
V02 = 0.35(20) + 0.061(20)(12)
= 7 + 14.64
= 21.64
32. Answer: 4.95 L-min-1
Solution:
V02 = 0.35(35) + 0.061(35)(20)
= 12.25 + 42.7
= 54.95 ml-min-l-kg
Convert to L-min-1: (54.95 x 90 kg)/1000 4.9455


33. Answer: 13.4 kcal-min-I

Solution:
V02 = 0.35(40) + 0.061(40)(10) = 14 + 24.4 = 38.4 ml-min-l-kg-1
Convert to L-min-1: (38.4 x 70 kg)/1000 = 2.688
2.688 x 5 kcal-min-1 = 13.4
34. Answer: 9.6 inches or approximately 3 platforms
Solution:
V02 1 1 METs x 0.85 x 3.5 = 32.7 ml-min-' kg-'
32.7 0.35(35) + 0.061(35)(height)
32.7 12.25 + 2.135(height)
20.45 = 2.135(height)
20.45/2.135 = height
9.58 = height
35. Answer: 56 beats-min-'
Solution:
Convert L-min-1 to ml-min-'.kg-1:
(1.6 x 1000)/90 = 17.8

17.8 = 0.35(rate) + 0,061(rate)(15)

17.8 = 0.35(rate) + 0.915(rate)

17.8 = 1.265(rate)
17.8/1.265 = rate
14 steps-minute-' = rate
Set the metronome at 4 x 14 = 56
36. Answer: 28.0 ml-min-'.kg-I
Solution:
V02 = 3.5(8 METS)
= 28.0
37. Answer: 10
Solution:

Calculate desired V02: 0.70 x 50 35 ml-min-l-kg-I 35 = 3.5(MET level) 35/3.5 = MET level 10 = MET level
38. Answer: 307 kcal
Solution:
Convert watts to kg-m-min-1: 150 x 6 900 kg.m.min-1


VO, = 3.5 + 2(900)/70

= 3.5 + 1800/70

= 3.5 + 25.71

= 29.21
Convert to L-min-1: (29.21 x 70)/1000 = 2.045 L-min-1
Convert to kcal-min-1: 2.045 X 5 = 10.225 kcal-min-1
10.225 x 30 minutes = 306.75
39. Answer: Level 1.9
Solution:
Calculate desired V02: 0.75 x 30 = 22.5 ml-min-'.kg-1
22.5 = 3.5 + 3(workload)/90

22.5 - 3.5 = 3(workload)/90
19 = 3(workload)/go
(19 X 90)/3 = workload
570 kg-m-min-1 = workload
Divide by 300 to get Airdyne level:
570/300 = 1.9
40. Answer: 15 mph

Solution:

Convert METS to ml-min-' -kg-': 8 X 3.5
28 = 3.5 + (tabled value)/60

28 - 3.5 = (tabled value)/60

24.5 X 60 = tabled value

1470 = tabled value

Our small cyclist is looking for a net V02 Of 1470 ml-min-'. According to Table 5.1, a speed of 15 mph yields a net V02 Of 1510 ml-min-'; close enough.

41. Answer: 160 bpm

Solution:
target HR = 0.75[(220 - 30) - 70] + 70 = 0.75(190 - 70) + 70 = 0.75(120) + 70 = 90 + 70 = 160
42. Answer: 99 bpm
Solution:
target HR = 0.45(120 - 82) + 82
= 0.45(38) + 82
= 17.1 + 82
= 99.1
28 ml-min-' kg-'
go


43. Answer: 179 bpm

Solution:

target HR = 0.85[(220 - 20) - 60] + 60

= 0.85(220 - 60) + 60

= 0.85(140) + 60

= 119 + 60

= 179
44. Answer: 123 bpm
Solution:
target HR = 0.82(220 - 70)
= 0.82(150)
= 123

45. Answer: 176

Solution:

target HR = 0.89(220 - 22)

= 0.89(198)

= 176.22

The target HR is 176 bpm. The number of beats that occurs in 1 0 seconds is one sixth this value: 176/6 = 29.34. Alternatively, you can look at Table 6.2 and find the 10-second count that most closely corresponds to the target HR.

46. Answer: 2.24 L-min-I

Solution:

Look it up in Table 7.1: 32 ml-min-'.kg-I

Convert to L-min-1: (32 x 70)/1000 = 2.24
47. Answer: 30 ml-min-'.kg-I
Solution:
V02max = [10.51(195) + 6.35(90) - 10.49(45) + 519.3]/90 = [2049.45 + 571.5 - 472.05 + 519.3]/90 = 2668.2/90
= 29.647
48. Answer: 23 ml-min-'.kg-1
Solution:
V02max = [6965.2 + 20.02(75) - 25.7(52) + 595.5(l) - 224(20.28) - 11.5(130)]/75 = [6965.2 + 1501.5 - 1336.4 + 595.5 - 4542.72 - 1495]/75 = 1688.08/75
= 22,508



49. Answer: 28 ml-min-'.kg-,

Solution:

From the Astrand nomogram, the raw V02MaX is approximately 2.4 L-min-1, and the age correction factor is 0.83. Thus, the absolute V02max is 2.4 x 0.83 = 1.992; the relative V02max is (1.992 x 1000)/70 = 28.457 ml-min-l-kg-1.

50. Answer: 21.3 ml-min-'.kg-I

Solution:

The age-predicted maximal HR is 220 - 30 = 190 bpm. By plotting HRs on the blank graph provided at the end of Chapter 7, the estimated maximal workload at that HR is 800 kg.m-min-1. Now we enter that into the cycle ergometry equation and solve for V02-

V02 = 3.5 + 2(800)/90

= 3.5 + 1600/90

= 21.278