SOLUTION: #64
To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per minute) should be in the target heart rate zone. The lower limit of this zone is
Question 81462: #64
To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per minute) should be in the target heart rate zone. The lower limit of this zone is found by taking 70% of the difference between 220 and your age. The upper limit is found by using 85%.
a) Find formulas for the upper and lower limits (u and I) as linear equations involving the age x.
b) what is the target heart rate zone for a 20-year-old?
c) What is the target heart rate zone for a 40-year-old?
d) Two women in an aerobics class stop to take their pulse, and are surpirsed to find that they have the same pulse. One women is 36years older than the other and is working at the upper limit of her target rate zone. The younger woman is working at the lower limit of hter target heart rate zone. What are the ages of hte two women, and what is their pulse?
You can put this solution on YOUR website! To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per minute) should be in the target heart rate zone. The lower limit of this zone is found by taking 70% of the difference between 220 and your age. The upper limit is found by using 85%.
a) Find formulas for the upper and lower limits (u and I) as linear equations involving the age x. Then y = heart rate:
:
Lower limit equation: y = .7(220-x)
Upper limit equation: y = .85(220-x)
:
:
b) what is the target heart rate zone for a 20-year-old?
:
Substitute 20 for x in the two equations:
Lower: y = .7(220 - 20) = 140
Upper: y = .85(220 - 20) = 170
:
:
c) What is the target heart rate zone for a 40-year-old?
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Do the same as above, substituting 40 for x
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d) Two women in an aerobics class stop to take their pulse, and are surprised to find that they have the same pulse. One women is 36years older than the other and is working at the upper limit of her target rate zone. The younger woman is working at the lower limit of her target heart rate zone. What are the ages of the two women, and what is their pulse?
:
Let x = age of the younger
Then (x+36) = age of the older
:
Younger's equation; y = .7(220-x); lower limit
Older's equation: y = .85(220 - (x+36)) = .85(220 - 36 - x) = .85(184-x)
:
Since they have equal pulses:
.7(220-x) = .85(184-x)
154 - .7x = 156.4 - .85x
+.85x - .7x = 156.4 - 154
.15x = 2.4
x = 2.4/.15
x = 16 yrs old is the younger
Then:
16 + 36 = 52 yrs old is the older
:
You can substitute these ages in the equations and determine what the pulses
actually are. Of course they should be equal
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A graph of this would look like this:
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Target rate is between the two graphs
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How about this? Make sense to you?
