Nita swam 4 laps in the pool in 14 min how long did it take her to swim 10 laps

Most of the information's that are required to solve the problem is already provided in the question.
Time taken by Nita to swim 4 laps = 14 minutes
Time taken by Nita to swim 10 laps = (14/4) * 10
                                                         = 7 * 5
                                                         = 35
So Nita will needs 35 minutes to swim 10 laps if her speed of swimming is the same. Hope I have answered the question in the manner you were looking for. This method is the only and easy method to solve such problems.

Let x = time in minutes it takes Nita to swim 10 laps
you can set up a proportion for this:

cross multiply to get:
4x=140
divide both sides by 4 to get your final
x=35
so to swim 10 laps in the pool, it took Nita 35 minutes

3x+9+4x+x=8x+9that's the answer for your question.