We know that
• Emma can dig a 13 ft by 6 ft hole in 8.5 hours.
,
• Kennedy can dig the same hole in 14 hours.
We are going to express the "hole" as unit 1 since both of them did one. The following rates express the job done for each person.
• Emma rate = 1/8.5 (job per hour)
,
• Kennedy rate = 1/14 (job per hour).
,
• The rate where they work together is 1/x.
Now, we form the equation with those rates

Then, we solve for x, we sum the fractions first

Now, we multiply in cross form

Then, we divide the equation by 22.5

Therefore, if they work together, they will finish the hole in 5 hours approximately.