Question 352481
Let b = speed of the biker
w = speed of the wind. 
This means b - w = speed of the biker relative to, and against, the wind 
Because {{{d = r*t}}}, we get {{{6*(b-w)=106}}}, or {{{b-w=53/3}}}.
Also, b + w = speed of the biker relative to, and in the same direction as, the wind.  So
{{{6*(b+w)=126}}}, or {{{b+w=21}}}.  So we have the system
{{{b-w=53/3}}}, and 
{{{b+w=21}}}.  
Solving this by elimination gives
{{{b=58/3}}} and {{{w=5/3}}}.
Therefore the speed of the wind is 5/3 miles per hour.