Question

How many more bpm was his heart rate while racing than while resting?

Answer 1

Hint: Heart rate is described as the number of heart beats per minute. The normal human heart rate ranges from 60-100 beats per minute (bpm). Lance Armstrong (pictured above) had a resting heart rate of 32 beats per minute. While racing, his heart rate would increase to 1.6 beats per second.

Formula used:
 \[{\Delta _{bpm}} = bp{m_{new}} - bp{m_{old}}\]

Complete step by step solution:
Given,
Lance Armstrong had a resting heart rate of 32 beats per minute.
While racing, his heart rate would increase to 1.6 beats per second.
Hence, we need to find the bpm of his heart rate while racing than while resting.
Using dimensional analysis, we need to convert 1.6 beats per second(bps) to beats per minute(bpm).
We get,
 \[\dfrac{{1.6beats}}{{\sec ond}} \cdot \dfrac{{60\sec onds}}{{\min }} = 1.6 \times 60bpm\]
Hence, evaluating we get:
 \[ \Rightarrow 96bpm\]
Hence, the change is:
 \[{\Delta _{bpm}} = bp{m_{new}} - bp{m_{old}}\]
Now, substitute the obtained value of heart rate with respect to given value as:
 \[{\Delta _{bpm}} = 96bpm - 32bpm\]
Simplifying the terms, we get:
 \[{\Delta _{bpm}} = 64bpm\]
Therefore, \[64bpm\] was his heart rate while racing than while resting.
So, the correct answer is “ \[64bpm\] ”.

Note: The key point to convert bps to bpm is using Dimensional analysis, it is essential because it keeps the units the same, helping us perform mathematical calculations smoothly and also, we use conversion factors to get the same units and we must also note that the dimensional analysis cannot help you determine any dimensionless constants in the equation.