Question 936211
let cyclist speed be x miles per hour
speed of the wind ( w) = 4 miles per hour
relative speed in the direction of wind  = x+4
relative speed against the direction of wind = x-4
distance traveled in the direction of wind = 8 miles
hence time taken = {{{ distance/speed}}}
                = {{{8/(x+4)}}}
distance traveled against the wind = 5 miles
  time taken ={{{ 5/(x-4)}}}
but time taken in both cases is same
   {{{ 8/(x+4) =5/(x-4)}}}
we have  to solve above equation