Respuesta :
Answer: The correct option is (b) [tex] 1\dfrac{7}{8}~\textup{hours}.[/tex]
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
[tex] \dfrac{1}{5}.[/tex]
Bailey can wash the dogs in 3 hours.
So, in 1 hour, the fraction of the dogs Bailey can wash is given by
[tex] \dfrac{1}{3}.[/tex]
Hence, if they work together, then the fraction of the dogs that they wash in 1 hour is given by
[tex] \dfrac{1}{5}+\dfrac{1}{3}=\dfrac{3+5}{15}=\dfrac{8}{15}.[/tex]
Therefore, the time taken by them to wash the dogs if they work together will be
[tex] t=\dfrac{1}{\frac{8}{15}}=\dfrac{15}{8}=1\dfrac{7}{8}~\textup{hours}.[/tex]
Thus, option (b) is correct.
