A football player is running the length of a 100 yard long football field. For the first part of the field, he runs at a rate of 2 yards per second. He sprints the last part of the field at a rate of 4 yards per second. If the whole run takes 40 seconds, what is the fraction of the length of the field that the runner covers during the second sprint?

Answer:[tex]\frac{2}{5}[/tex]th part of the field is covered in the second sprint.Step-by-step explanation:A football player is running the length of a 100 yard long football field.Let player sprints x yards with the speed = 2 yards per second.So time taken to cover x yards player will take time = [tex]\frac{x}{2}[/tex] secondsNow rest distance (100 - x) yards when covered with the speed of 4 yards per second, so time taken to cover this distance = [tex]\frac{Distance}{Speed}[/tex]= [tex]\frac{100-x}{4}[/tex] secondsNow total time taken by the player can be represented by the equation [tex]\frac{x}{2}+\frac{100-x}{4}=40[/tex]Now we can solve this equation for the value of x.[tex]\frac{2x+100-x}{4}=40[/tex]x + 100 = 40×4x + 100 = 160x = 160 - 100 = 60 yardsAnd length of the second part will be = 100 - 60 = 40 yardsNow the fraction of the field covered by the player in second sprint will be = [tex]\frac{40}{100}[/tex]= [tex]\frac{2}{5}[/tex] or 40%Therefore, [tex]\frac{2}{5}[/tex]th part of the field was covered in second sprint.