Maria is planning to participate in the Triathlon-Brazil, which consists of $800 \mathrm{~m}$ of swimming, followed by $20 \mathrm{~km}$ of cycling, and finally, $4 \mathrm{~km}$ of running. Maria runs at a constant speed that is three times the speed at which she swims and cycles 2.5 times faster than she runs. To finish the race in no more than 1 hour and 20 minutes, what must be her minimum speed in each of the three disciplines?
Let $x$ be the speed at which Maria swims, in meters per minute. Then the time Maria spends swimming $800 \mathrm{~m}$ is given by $800 / x$ minutes. We know that her running speed is $3 x$ and, on the bicycle, $2.5 \times 3 x=7.5 x$ meters per minute. Thus, the total time Maria spends on the three stages is

$$
\underbrace{\frac{800}{x}}_{\text {swimming }}+\underbrace{\frac{20000}{7.5 x}}_{\text {cycling }}+\underbrace{\frac{4000}{3 x}}_{\text {running }}=\frac{800 \times 7.5+20,000+4000 \times 2.5}{7.5 x}=\frac{4800}{x}
$$

minutes. Therefore, for her to complete the three stages in, at most, one hour and twenty minutes, or $80 \mathrm{~min}$, we must have, at a minimum, $80=4800 / x$, or $x=4800 / 80=60$ meters per minute. It follows that $3 x=180$ and $7.5 x=450$ meters per minute. Thus, for Maria to finish the race in, at most, 1 hour and 20 minutes, she must achieve the following minimum speeds:

- swim at a minimum speed of $60 \mathrm{~m} / \mathrm{min}$,
- cycle at a minimum speed of $450 \mathrm{~m} / \mathrm{min}$ and
- run at a minimum speed of $180 \mathrm{~m} / \mathrm{min}$.