How to find total climbing time based on Rate of Climb?
The fastest way is an integration. If you plot the inverted climb speed over altitude like in the plot below, the area under the curve will give you the time to climb. I would suggest you calculate the climb speed at every 1000&nbsp;m by rule of proportion — at sea level it is 20.87&nbsp;m/s and at 11.000&nbsp;m it is 0&nbsp;m/s. Then you get a plot like the one below. The red circles are the calculated points; the lines between them are straight interpolations.

Since the unit on the Y-axis is seconds per meter and the unit on the X-axis is meters, the area is in seconds. Just calculate the area of each trapezoid between the start and the end altitudes and add them. In the figure below I have crosshatched the trapezoids between 3000&nbsp;m and 8000&nbsp;m. 



Inverted climb speed over altitude plot. Caution — this is a generic plot I did for this purpose earlier, so it uses different numbers. I crosshatched the area between 3000&nbsp;m and 8000&nbsp;m, because I made the plot for calculating the climb time from 3000&nbsp;m to 8000&nbsp;m.