Answer:
Time taken by Juanita and mark to cater meals is 11.08 hours or 11 hours 4 minutes and 13.08 hours or 13 hours 4 minutes respectively.
Solution:
Given, Together, Juanita and Mark can make preparations to cater a dinner in 6 hours.
Alone, Juanita can do the job 2 hours faster than Mark.
We need to find the time that each person takes to prepare to cater a meal.
Let the time taken by Juanita be x hours.
Then time taken by mark becomes x + 2 hours.
Now, work done by Juanita in 1 hour =
[by assuming total work done as 1 unit]
And, work done by mark in 1 hour =

Together, in one hour they can complete
work, which equals to
[ as given that together they completed in 6 hours ]

Now, by using quadratic formula,


We can neglect
as time cannot be negative.

= 11.08 approximately
So, Juanita completes work alone in 11.08 hours or 11 hours 4 minutes approximately.
So, mark completes work in 11.08 + 2 = 13.08 hours or 13 hours 4 minutes approximately.
Hence, time taken by Juanita and mark to cater meals is 11.08 hours or 11 hours 4 minutes and 13.08 hours or 13 hours 4 minutes respectively.