<PRE><B>Question 254771</B>
Given, the speed of the bicycle = 15 miles per hour 
Let the speed of the wind = x miles per hour
A bicycle traveling at a constant speed goes 45 miles with the wind turns around and travels an additional 42 miles against the wind.
Time taken to travel with the wind = distance/speed
                                   = 45/(15+x)
Time taken to travel against the wind = 42/(15-x)
Total time is 45/(15+x) +42/(15-x) = 6
              [45(15-x)+42(15+x)]/(15-x)(15+x)= 6
               675-45x+630+42x = 6(15+x)(15-x)
               -3x+1305 = 6(225-x^2)
                      0 = 1350-6x^2+3x-1305
           6x^2-3x-45=0
           2x^2-x-15 = 0
         (2x+5)(x-3) = 0
                   x = 3, -5/2
Since x cannot be negative, we get x = 3
Therefore the speed of the wind = 3 miles per hour

           
             
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