A block is pulled with constant tension up an incline, find the distance?

[clesling]

Homework Statement

A mass m = 13kg is pulled along a horizontal floor with no friction for a distance of d = 5.1m. Then the mass is pulled up an incline that makes an angle theta = 39 degrees with the horizontal and has a coefficient of kinetic friction u = 0.39. The entire time the massless rope is used to pull the block is pulled parallel to the incline at an angle of theta = 39 degrees (thus on the incline it is parallel to the surface) and has a tension of 68 N. How far up the incline does the block travel before coming to rest (measured along the incline)?

Homework Equations

I have answered the following questions and found these values to be correct.

The work done by tension before the block goes up the incline (on the horizontal surface) to be 269.5 Joules
The speed of the block right before it begins to travel up the incline is 6.4392 m/s
The work done by friction after a specific distance of x = 2.1 m up the incline (for x measured along the incline) is -81.171 Joules
The work done by gravity after the block has traveled a specific distance of x = 2.1m (for x measured along the incline) is -168.54 Joules

The Attempt at a Solution

I have attempted to incorporate the above ideas and answers into the solution, but have no idea if any of these answers are relevant to the final question which is to find the total distance traveled by the object up the incline.

 

[tiny-tim]

hi clesling!

A mass m = 13kg is pulled along a horizontal floor with no friction for a distance of d = 5.1m. Then the mass is pulled up an incline that makes an angle theta = 39 degrees with the horizontal and has a coefficient of kinetic friction u = 0.39. The entire time the massless rope is used to pull the block is pulled parallel to the incline at an angle of theta = 39 degrees (thus on the incline it is parallel to the surface) and has a tension of 68 N. How far up the incline does the block travel before coming to rest (measured along the incline)?
…
I … have no idea if any of these answers are relevant to the final question which is to find the total distance traveled by the object up the incline.

yes, use the work-energy theorem …

work done = change in mechanical energy ​

(mechanical energy is KE + PE)