Tom is 25 years old, and likes to keep fit by exercising. (a) Use this formula to find his maximum heart rate (bpm). Maximum heart rate = 220 - age in years Tom's maximum heart rate is ______________________________ bpm. (b) Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate. Between what two heart rates should Tom be aiming for to get the most benefit from his exercise?

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Tom is 25 years old, and likes to keep fit by exercising - HSC - SSCE Mathematics Standard - Question 16 - 2022 - Paper 1

Question 16

Tom is 25 years old, and likes to keep fit by exercising. (a) Use this formula to find his maximum heart rate (bpm). Maximum heart rate = 220 - age in years Tom's... show full transcript

Worked Solution & Example Answer:Tom is 25 years old, and likes to keep fit by exercising - HSC - SSCE Mathematics Standard - Question 16 - 2022 - Paper 1

Step 1

Use this formula to find his maximum heart rate (bpm).

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Answer

To find Tom's maximum heart rate, we can use the formula:

ext{Maximum heart rate} = 220 - ext{age}

Substituting Tom's age:

= 220 - 25 = 195 ext{ bpm}

Therefore, Tom's maximum heart rate is 195 bpm.

Step 2

Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate.

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Answer

To determine the heart rates for maximum benefit:

Calculate 50% of Tom's maximum heart rate:
$50 ext{% of } 195 = 0.5 imes 195 = 97.5 ext{ bpm}$
Calculate 85% of Tom's maximum heart rate:
$85 ext{% of } 195 = 0.85 imes 195 = 165.75 ext{ bpm}$

Thus, Tom should aim for a heart rate between 97.5 bpm and 165.75 bpm for optimal exercise benefits.

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