Running at a speed of $10 \mathrm{~km} / \mathrm{h}$, João completes a certain course in six minutes. At what speed, in $\mathrm{km} / \mathrm{h}$, can he complete the same course in eight minutes?
(a) 7.5
(b) 7.75
(c) 8
(d) 8.25
(e) 8.5
The correct option is (a).

Solution 1: The distance traveled is $d=10 \frac{\mathrm{km}}{\mathrm{h}} \times 6 \min =10 \frac{\mathrm{km}}{\mathrm{h}} \times 6 \times \frac{1}{60} \mathrm{~h}=1 \mathrm{~km}$.

Traveling the same distance of $1 \mathrm{~km}$ in 8 minutes, the speed will be

$$
v=\frac{1 \mathrm{~km}}{8 \mathrm{~min}}=\frac{1 \mathrm{~km}}{8 \times \frac{1}{60} \mathrm{~h}}=\frac{60}{8} \mathrm{~km} / \mathrm{h}=\frac{15}{2} \mathrm{~km} / \mathrm{h}=7.5 \mathrm{~km} / \mathrm{h}
$$

Solution 2: We can directly use the rule of three, as follows.

Speed in $\mathrm{km} / \mathrm{h}$

10

$x$
Time in hours

$$
\begin{aligned}
& \rightarrow \quad \frac{6}{60} \\
& \rightarrow \quad \frac{8}{60}
\end{aligned}
$$

Speed and time are inversely proportional (increasing speed decreases time), so $x / 10=\left(\frac{6}{60}\right) /\left(\frac{8}{60}\right)=6 / 8$, therefore, $x=60 / 8$, that is, the speed will be

$$
x=\frac{60}{8} \mathrm{~km} / \mathrm{h}=\frac{15}{2} \mathrm{~km} / \mathrm{h}=7.5 \mathrm{~km} / \mathrm{h}
$$