142. Which of the numbers is larger: $2^{3^{2^{3}}}$ or $3^{2^{3^{2}}}$?
Solution. Since, on the one hand, $2^{3^{8}}>2^{3^{7} \cdot 2}=4^{3^{7}}>3^{3^{7}}$, and on the other hand, $3^{7}>3^{6}>729>2^{9}$, then $3^{3^{7}}>3^{2^{9}}$. Therefore, the first of the given numbers in the problem is greater than the second.

143(1171)'. Two cars, moving along a circular road at constant speeds in the same direction, are side by side every 56 minutes. When moving at the same speeds in opposite directions, the cars meet every 8 minutes. How long will it take each car to travel the entire circular road?

Solution. Let $s$ (m) be the length of the circular road, $v_{1}$ (m/min) be the speed of the first car, and $v_{2}$ (m/min) be the speed of the second car. According to the problem, we can set up the following system of equations:

' For problems 143-146, the numbers in parentheses are the exercise numbers in textbook $|8|$.

$$
\left\{\begin{array}{l}
56\left(v_{1}-v_{2}\right)=s \\
8\left(v_{1}+v_{2}\right)=s
\end{array}\right.
$$

from which $v_{1}=\frac{s}{14}$ (m/min), $v_{2}=\frac{6 s}{112}$ (m/min).

Then the first car will travel the entire circular road in 14 minutes $\left(s: \frac{s}{14}=14\right)$, and the second car will take 18 minutes 40 seconds $\left(s: \frac{6 s}{112}=18 \frac{2}{3}\right)$.

Answer: 14 minutes; 18 minutes 40 seconds.