Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same while in six hours. How long would it take them if they worked together?

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 .  

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 .

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 .

Since they will work together, so we can equate sum of work completed by both as:

Therefore, it will take hours to dig the pool working together.

so, converting firstly the mixed fractions to improper fractions and then "adding".