In a relay competition, where each team has two athletes, each athlete runs $21 \mathrm{~km}$ and the second athlete only starts running when the first athlete finishes their part and passes the baton. The record for this competition is 2 hours and 48 minutes. In João and Carlos's team, João starts the race and runs his part at a speed of $12 \mathrm{~km} / \mathrm{h}$. To break the record, what must be Carlos's speed?
Since speed $=\frac{\text { distance }}{\text { time }}$, or equivalently, time $=$ $\frac{\text { distance }}{\text { speed }}$, the time spent by João was

$$
t=\frac{21}{12} \mathrm{~h}=\left(1+\frac{9}{12}\right) \mathrm{h}=1 \mathrm{~h}+\frac{9}{12} \times 60 \mathrm{~min}=1 \mathrm{~h} 45 \min
$$

Therefore, Carlos needs to complete the race in a time less than

$$
(2 \mathrm{~h} 48 \mathrm{~min})-(1 \mathrm{~h} 45 \mathrm{~min})=1 \mathrm{~h} 3 \mathrm{~min}=63 \mathrm{~min}
$$

For this, his speed $v$, in $\mathrm{km} / \mathrm{min}$, must satisfy $\frac{21}{v}=t\frac{21}{63}=\frac{1}{3} \mathrm{~km} / \mathrm{min}=\frac{60}{3} \mathrm{~km} / \mathrm{h}=20 \mathrm{~km} / \mathrm{h}
$$

Therefore, Carlos must run at a speed greater than $20 \mathrm{~km} / \mathrm{h}$.