Answer: The correct option is (b) ![1\dfrac{7}{8}~\textup{hours}.](https://tex.z-dn.net/?f=%201%5Cdfrac%7B7%7D%7B8%7D~%5Ctextup%7Bhours%7D.)
Step-by-step explanation: Given that Abigail and Bailey wash dogs to make extra money. Abigail can wash all of the dogs in 5 hours and Bailey can wash all the dogs in 3 hours.
We are to find the time taken by them if they wash the dogs together.
Abigail can wash the dogs in 5 hours.
So, in 1 hour, the fraction of the dogs Abigail can wash is given by
![\dfrac{1}{5}.](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B5%7D.)
Bailey can wash the dogs in 3 hours.
So, in 1 hour, the fraction of the dogs Bailey can wash is given by
![\dfrac{1}{3}.](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B3%7D.)
Hence, if they work together, then the fraction of the dogs that they wash in 1 hour is given by
![\dfrac{1}{5}+\dfrac{1}{3}=\dfrac{3+5}{15}=\dfrac{8}{15}.](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B5%7D%2B%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B3%2B5%7D%7B15%7D%3D%5Cdfrac%7B8%7D%7B15%7D.)
Therefore, the time taken by them to wash the dogs if they work together will be
![t=\dfrac{1}{\frac{8}{15}}=\dfrac{15}{8}=1\dfrac{7}{8}~\textup{hours}.](https://tex.z-dn.net/?f=%20t%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7B8%7D%7B15%7D%7D%3D%5Cdfrac%7B15%7D%7B8%7D%3D1%5Cdfrac%7B7%7D%7B8%7D~%5Ctextup%7Bhours%7D.)
Thus, option (b) is correct.