Question 701751
The tugboat going upstream is slowed by 5 mph, so speed is r-5 mph; letting r equal speed in still water.  The tugboat going downstream is going WITH the current and its speed is increased by 5 mph, so speed is r+5 mph.
Let t = time in hours.

One can make a table using this format:


Which Direction: Speed(miles per hour), Time(hours), Distance(miles)
Upstream:     r-5, t, 30
Downstream:   r+5, t, 6


Find two expressions for the travel time, which are equal for the both boats.
Upstream,  {{{t=30/(r-5)}}}
Downstream,  {{{t=6/(r+5)}}}


The formulas for t are equal, so  

{{{30/(r-5)=t=6/(r+5)}}}

Most of the effort is analyzing the situation and setting up the relationship equation.  Solve for r.