Answer:
6.6 mi/h
Step-by-step explanation:
Given,
For first 16.5 miles, speed is 21.8 miles per hour,
Since,
![Time = \frac{Distance}{Speed}](https://tex.z-dn.net/?f=Time%20%3D%20%5Cfrac%7BDistance%7D%7BSpeed%7D)
So, the time taken in first time = ![\frac{16.5}{21.8}](https://tex.z-dn.net/?f=%5Cfrac%7B16.5%7D%7B21.8%7D)
Let x be the average speed in miles per hour for another 5.5 miles,
So, the time taken in second time = ![\frac{5.5}{x}\text{ hours}](https://tex.z-dn.net/?f=%5Cfrac%7B5.5%7D%7Bx%7D%5Ctext%7B%20hours%7D)
∴ Total time taken in entire journey = ![\frac{16.5}{21.8}+\frac{5.5}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B16.5%7D%7B21.8%7D%2B%5Cfrac%7B5.5%7D%7Bx%7D)
Now, total distance covered = 16.5 + 5.5 = 22 miles,
Hence, the average speed for the entire race = ![\frac{22}{\frac{16.5}{21.8}+\frac{5.5}{x}}](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7B%5Cfrac%7B16.5%7D%7B21.8%7D%2B%5Cfrac%7B5.5%7D%7Bx%7D%7D)
According to the question,
![\frac{22}{\frac{16.5}{21.8}+\frac{5.5}{x}}=13.8](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7B%5Cfrac%7B16.5%7D%7B21.8%7D%2B%5Cfrac%7B5.5%7D%7Bx%7D%7D%3D13.8)
![22=13.8(\frac{16.5}{21.8}+\frac{5.5}{x})](https://tex.z-dn.net/?f=22%3D13.8%28%5Cfrac%7B16.5%7D%7B21.8%7D%2B%5Cfrac%7B5.5%7D%7Bx%7D%29)
![22=\frac{227.7}{21.8}+\frac{75.9}{x}](https://tex.z-dn.net/?f=22%3D%5Cfrac%7B227.7%7D%7B21.8%7D%2B%5Cfrac%7B75.9%7D%7Bx%7D)
![22-\frac{117.7}{21.8}=\frac{75.9}{x}](https://tex.z-dn.net/?f=22-%5Cfrac%7B117.7%7D%7B21.8%7D%3D%5Cfrac%7B75.9%7D%7Bx%7D)
![\frac{361.9}{21.8}=\frac{75.9}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B361.9%7D%7B21.8%7D%3D%5Cfrac%7B75.9%7D%7Bx%7D)
![\implies x = 6.56856\approx 6.6\text{ miles per hour}](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%206.56856%5Capprox%206.6%5Ctext%7B%20miles%20per%20hour%7D)