Math II (Несколько текстов для зачёта), страница 27

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Fig. 1 One student's solution to the activity sheet

Running by the Numbers Activity Sheet

NAME -----

1. An athlete's maximum exertion heart rate is calculated by subtracting his or her age from a fixed number: 220 for males and 226 for females. For example, a 24-year-old female runner has a maximum exertion heart rate of 202 beats per minute, or 226 - 24 = 202. The target performance heart rate is 80% of maximum. Calculate the target performance heart rate for the following runners:

a. 14-year-old female

b. 23-year-old male

c. 35-year-old female

d. 49-year-old male

e. yourself

2. A runner follows the training schedule in the table below.

DAY 1 DAY 2 DAY 3 DAY 4 DAY 5

5 km 7.5 km 10 km 5 km Rest

If the runner maintains an average rate of 8 km/hr., how much time does he spend training in one year?

3. A runner trained for three days in a row. On day 1, she ran 7.5 km in 37 minutes. On day 2, she ran 8.3 km in 41 minutes. On day 3, she ran 6.8 km in 32 minutes. What was her average pace expressed in km/hr. and in m/sec.?

4. The record for the Math-at-Work 5-km Mini-Marathon is 38 minutes and 12 seconds. What is the likely finishing time for the runner in question 3?

5. One mile is approximately 1.6 km. How many miles does the runner in question 3 run in training in one year?

Fig. 1 One student's solution to the activity sheet

1. a) Max.: 226 - 14 = 212

Target: 0.8 x 212 = 169.6 congruent to 170

b) Max.: 220 - 23 = 197

Target: 0.8 x 197 = 157.6 congruent to 158

c) Max.: 226 - 35 = 191

Target: 0.8 x 191 = 152.8 congruent to 153

d) Max.: 220 - 49 = 171

Target: 0.8 x 171 = 136.8 congruent 137

e) Max.: 226 - 13 = 213

Target: 0.8 x 213 = 170.4 congruent 170

2. Total distance ran: 5 km + 7.5 km + 10 km + 5 km = 27.5 km

Therefore 27.5 km/8 km/hr. = 3.44 hrs.

Number of 5-day cycles within a year: 365 days/5 days = 73 5-day

cycles.

(This character cannot be represented in ASCII text) The total

amount of time the runner spends on training in one year = 3.44

hrs. x 73 5-day cycles = 251.12 hrs.

3. Total distance: 7.5 km + 8.3 km + 6.8 km = 22.6 km

Total time: 37 min. + 41 min. + 32 min. = 110 min.

110 min./60 min. = 1.83 hrs.

Therefore Average pace (km/hr.) = 22.6 km/1.83 hrs.

= 12.35 km/hr.

Average pace (m/sec): 12.35 km x 1 000 = 12 350 m

1 hour = 3 600 sec.

then 12 350 m/3 600 sec. = 3.43 m/s

Therefore Average pace (m/sec.): 3.43 m/sec.

4. Time = distance/speed = 5 km/12.35 km/hr. =0.405 hrs. = 24.30

min.

= 24 min. 18 sec.

5. Total distance: 7.5 km + 8.3 km + 6.8 km = 22.6 km

Therefore Total distance (miles) = 22.6 km/1.6 km = 14.125 miles

Amount of 3-day cycles in a year: 365/3 = 121.67

Therefore Total amount of miles ran in training in one year:

14.125 miles x 121.67 = 1718.59 miles