Question

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 1

`(2)/(5)`th part of the field is covered in the second sprint.

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 =
`(x)/(2)` seconds

Now rest distance (100 - x) yards when covered with the speed of 4 yards per second, so time taken to cover this distance =
`(Distance)/(Speed)`

=
`(100-x)/(4)` seconds

Now total time taken by the player can be represented by the equation

`(x)/(2)+(100-x)/(4)=40`

Now we can solve this equation for the value of x.

`(2x+100-x)/(4)=40`

x + 100 = 40×4

x + 100 = 160

x = 160 - 100 = 60 yards

And length of the second part will be = 100 - 60 = 40 yards

Now the fraction of the field covered by the player in second sprint will be

=
`(40)/(100)`

=
`(2)/(5)` or 40%

Therefore,
`(2)/(5)`th part of the field was covered in second sprint.