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Target heart rate is determined by multiplying the reserve heart rate by the training intensity level, p, where 0 <= p <= 1, and adding the resting heart rate. An adult woman with a resting heart rate of 65 beats per minute (bpm) and a reserve heart rate of 125bpm is told by a trainer that her target heart rate should not exceed 140bpm. What is the maximum training intensity level, p, that is consistent with her trainer's advice?

Target heart rate is determined by multiplying the reserve heart rate by the training intensity level, p p , where 0≤p≤1 0 \leq p \leq 1 , and adding the resting heart rate. An adult woman with a resting heart rate of 6565 beats per minute (bpm) and a reserve heart rate of 125bpm 125 \mathrm{bpm} is told by a trainer that her target heart rate should not exceed 140bpm 140 \mathrm{bpm} . What is the maximum training intensity level, p p , that is consistent with her trainer's advice?

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Q. Target heart rate is determined by multiplying the reserve heart rate by the training intensity level, p p , where 0≤p≤1 0 \leq p \leq 1 , and adding the resting heart rate. An adult woman with a resting heart rate of 6565 beats per minute (bpm) and a reserve heart rate of 125bpm 125 \mathrm{bpm} is told by a trainer that her target heart rate should not exceed 140bpm 140 \mathrm{bpm} . What is the maximum training intensity level, p p , that is consistent with her trainer's advice?
  1. Understand formula for target heart rate: Understand the formula for target heart rate.\newlineThe target heart rate is calculated by the formula: \newlineTarget Heart Rate=(Reserve Heart Rate×p)+Resting Heart Rate\text{Target Heart Rate} = (\text{Reserve Heart Rate} \times p) + \text{Resting Heart Rate},\newlinewhere pp is the training intensity level.
  2. Insert given values into formula: Insert the given values into the formula.\newlineThe woman's resting heart rate is 6565 bpm, and her reserve heart rate is 125125 bpm. Her target heart rate should not exceed 140140 bpm. So we have the equation: 140=(125×p)+65140 = (125 \times p) + 65.
  3. Isolate pp: To find pp, we need to isolate it on one side of the equation. \newlineFirst, subtract the resting heart rate from both sides of the equation: \newline140−65=(125×p)+65−65140 - 65 = (125 \times p) + 65 - 65\newline75=125×p75 = 125 \times p
  4. Solve for pp: Divide both sides by 125125 to solve for pp.p=75125p = \frac{75}{125}
  5. Calculate value of p: Divide 7575 by 125125.\newlineCalculation: p=75125=0.6p = \frac{75}{125} = 0.6

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