Question 769071
Make a speed, time, distance table for all of the data and any that you can express from the given data.


Let r = speed of the guide if rowing in still water.
When you say, "6 mi down the river and back", this is 6 miles up the river and 6 miles down the river.  Round trip up and back is 12 miles.  If you believe this is the wrong interpretation then say so.



DIRECTION________speed___________time hours________distance miles
DOWN RIVER_______r+4_____________(___)________________6
UP RIVER_________r-4_____________(___)________________6


The key relation speed*time=distance allows us to make expressions to fill-in times.  
r*h=d for {{{speed*timeHours=distanceMiles}}}
{{{timeHours=distanceMiles/speed}}}



DIRECTION________speed___________time hours________distance miles
DOWN RIVER_______r+4_____________(6/(r+4))________________6
UP RIVER_________r-4_____________(6/(r-4))________________6
TOTAL______________________________2_____________________12


He rows up and back in 2 hours.  This allows us to equate to the sum of the time expressions and the only unknown variable is r.

{{{highlight(6/(r+4)+6/(r-4)=2)}}} The problem's principle resulting equation to solve.  The rest of the process is for you to do.