# 4. Having covered half of the distance, the train reduced its speed by $25 \%$ and therefore arrived at the destination 0.5 hours late. How long did it take the train to cover the entire distance?
Solution Let the total distance be S. Let X km/h be the speed of the train when it travels the first half of the distance. Then $0.75 \mathrm{x}$ km/h is the speed of the train when it travels the second half of the distance. Therefore, $\frac{0.5 S}{\mathrm{x}}$ hours were spent by the train on the first half of the journey, $\frac{0.5 S}{0.75 x}$ hours on the second half, and $\frac{S}{x}$ hours are required for the train to travel the entire distance at a constant speed of $\mathrm{x}$ km/h.

According to the problem, we have the equation

$$
\frac{0.5 S}{x}+\frac{0.5 S}{0.75 x}=\frac{S}{x}+0.5
$$

solving which, we find $x=3.5$.

Answer: 3.5 hours