Solution:
Let the speed of cyclist without any wind = x miles per hour
Speed of cyclist when speed of wind increases by 2 miles per hour = (x + 2 )miles per hour
Also , relation that is given between speed of cyclist without wind and with wind is :Riding with the wind at her back, a cyclist takes an hour less time to cover 80 miles than without any wind.
Converting this statement into terms of equation:
[tex]\frac{80}{x}-\frac{80}{x+2}=1 \\\\ 160 = x^2 + 2x \\\\ x^2 + 2x - 160=0 \\\\ x= \frac{-2\pm\sqrt{4+640}}{2}, {\text {As speed can't be negative, so taking positive value of x}} Gives, x =11.68[/tex]→→→To solve the Quadratic equation of type : a x² + b x + c=0, I have used discriminant method, to find the roots, which is x= [tex]\frac{-b\pm\sqrt{D=b^2-4ac}}{2a}[/tex]
Speed of cyclist without wind = 11.68 miles per hour
Speed of cyclist when wind is flowing = 11.68 +2 = 13.68 miles per hour
