9) A very regular sprinter, when running 100 meters, takes 2.4 seconds for the first 20 meters and runs the remaining $80 \mathrm{~m}$ at a constant speed, finishing the race in 10 seconds exactly. If he continued for another $100 \mathrm{~m}$ without changing his speed, what time would he achieve on the $200 \mathrm{~m}$ ?
(A) $18.8 \mathrm{~s}$
(B) $19 \mathrm{~s}$
(C) $19.5 \mathrm{~s}$
(D) $19.6 \mathrm{~s}$
(E) $20 \mathrm{~s}$.
9) The answer is $\mathbf{( C )}$.

![](https://cdn.mathpix.com/cropped/2024_04_17_23f072eac9b2d02bc457g-2.jpg?height=280&width=323&top_left_y=174&top_left_x=1592)

The speed the athlete maintains in the last $80 \mathrm{~m}$ is given by $v=\frac{80}{10-2.4} \mathrm{~m} / \mathrm{s}=\frac{80}{7.6} \mathrm{~m} / \mathrm{s}$.

Therefore, to cover another 100 meters at the same speed, the athlete takes $100 \cdot \frac{7.6}{80} \mathrm{~s}=\frac{76}{8} \mathrm{~s}=9.5 \mathrm{~s}$. The total time to cover $200 \mathrm{~m}$ will then be $19.5 \mathrm{~s}$.