Answer: 8.4 miles per hour
Step-by-step explanation:
Since, total distance = 24.5 miles,
Time taken = ![175 \text{ minutes} = \frac{175}{60} \text{ hours} =\frac{35}{12} \text{ hours}](https://tex.z-dn.net/?f=175%20%5Ctext%7B%20minutes%7D%20%3D%20%5Cfrac%7B175%7D%7B60%7D%20%5Ctext%7B%20hours%7D%20%3D%5Cfrac%7B35%7D%7B12%7D%20%5Ctext%7B%20hours%7D)
Thus,
![\text{ The unit rate} = \frac{\text{ Total distance}}{\text{ Time taken}}](https://tex.z-dn.net/?f=%5Ctext%7B%20The%20unit%20rate%7D%20%3D%20%5Cfrac%7B%5Ctext%7B%20Total%20distance%7D%7D%7B%5Ctext%7B%20Time%20taken%7D%7D)
![=\frac{24.5}{35/12}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B24.5%7D%7B35%2F12%7D)
![=\frac{294}{35}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B294%7D%7B35%7D)
![=8.4\text{ miles per hour}](https://tex.z-dn.net/?f=%3D8.4%5Ctext%7B%20miles%20per%20hour%7D)
Let n be old painters time. Then the new painters are 2n. So:
1/n+1/2n=1/6
2+1=2n/6
2n=18
n=9
The old painters take 9 hours; the new ones take 18
☺☺☺☺
The answer to the problem is 8