Respuesta :
Answer:
The average speed using harmonic mean is 61.08 miles per hour.
Step-by-step explanation:
We are given the following in the question:
52 miles per hour for 100 miles, then, 74 miles per hour for 100 miles.
We have to use harmonic mean to find the average speed.
Relation:
[tex]\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]
Total time:
[tex]t_1 = \dfrac{100}{52}\text{ hours}\\\\t_2=\dfrac{100}{74}\text{ hours}[/tex]
Total distance:
[tex]d_1 = 100\text{ miles}\\d_2 = 100\text{ miles}[/tex]
Average speed:
[tex]s=\dfrac{\text{Total distance}}{\text{Total time}}\\\\s = \dfrac{100+100}{\frac{100}{52}+\frac{100}{74}}\\\\s = 61.08\text{ miles per hour}[/tex]
Harmonic mean =
[tex]s=\dfrac{n}{\sum (\frac{1}{x_i})}\\\\s = \dfrac{2}{\frac{1}{52}+\frac{1}{74}}\\\\s = 61.08[/tex]
Thus, the average speed using harmonic mean is 61.08 miles per hour.
