Answer :
Answer:
[tex]2\frac{8}{11}[/tex] hours.
Step-by-step explanation:
Let t represent time taken in hours by both working together.
So part of work completed by working together in 1 hour would be [tex]\frac{1}{t}[/tex].
We have been given that working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. So part of work completed by Ryan in 1 hour would be [tex]\frac{1}{5}[/tex].
We are also told that Castel can dig the same while in six hours. So part of work completed by Castel in 1 hour would be [tex]\frac{1}{6}[/tex].
Since they will work together, so we can equate sum of work completed by both as:
[tex]\frac{1}{t}=\frac{1}{6}+\frac{1}{5}[/tex]
[tex]\frac{1}{t}\times 30t=\frac{1}{6}\times 30t+\frac{1}{5}\times 30t[/tex]
[tex]30=5t+6t[/tex]
[tex]30=11t[/tex]
[tex]11t=30[/tex]
[tex]\frac{11t}{11}=\frac{30}{11}[/tex]
[tex]t=2\frac{8}{11}[/tex]
Therefore, it will take [tex]2\frac{8}{11}[/tex] hours to dig the pool working together.