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Lana71 [14]
3 years ago
5

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?
Mathematics
1 answer:
notka56 [123]3 years ago
5 0

Answer:

\frac{2}{5}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 = \frac{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 = \frac{Distance}{Speed}

= \frac{100-x}{4} seconds

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

\frac{x}{2}+\frac{100-x}{4}=40

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

\frac{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

= \frac{40}{100}

= \frac{2}{5} or 40%

Therefore, \frac{2}{5}th part of the field was covered in second sprint.

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