Problem Statement
Kevin is trying to keep his heart rate at 160 beats/minute and in his workout, he counts 14 beats in 6 seconds. We are asked to find:
1. How many beats per minute is 14 beats in 6 seconds
2. Should he work out a little bit more?
Solution
- During Kevin's workout, we are told that he counts 14 beats in 6 seconds. We need to convert this to beats per minute so that we can compare it with 160 beats per minute.
- To convert 14 beats in 6 seconds to beats per minute, we would follow the pattern as follows:
Kevin counts 14 beats in the first 6 seconds
Kevin would count 2(14) = 28 beats in the first 6(2) = 12 seconds
Kevin would count 3(14) = 42 beats in the first 6(3) = 18 seconds
- We can generalize this pattern as follows:
Kevin would count n(14) = 14n beats in the first 6(n) = 6n seconds.
- This implies that if we want to know the number of beats his heart would go for every 1 minute, we simply need to find the number of beats for 60 seconds.
Thus, we can find the value of n by equating 6n seconds to 60 seconds.
[tex]\begin{gathered} 6n=60 \\ \text{divide both sides by 6} \\ \frac{6n}{6}=\frac{60}{6} \\ \\ n=10 \end{gathered}[/tex]- If n is 10, then we can use our general statement to find the number of beats Kevin's heartbeats per minute.
- Kevin would count 10(14)= 140 beats in the first 6(10) = 60 seconds= 1 minute.
Answer to Question 1
- Thus, Kevin's heat rate is 140 beats per minute
Answer to Question 2
-
