## Task 4 - 330734

Ulrike is sitting by the window of a train traveling at a speed of $60 \frac{\mathrm{km}}{\mathrm{h}}$. She observes that a train traveling in the opposite direction passes by her window in 4 seconds. She also knows that this oncoming train is $120 \mathrm{~m}$ long.

Determine whether the speed of the oncoming train can be uniquely determined from this information! If so, give this speed in $\frac{\mathrm{km}}{\mathrm{h}}$!
The distance covered by the oncoming train in 4 seconds is obtained by reducing its length $120 \mathrm{~m}$ by the length of the distance covered by Ulrike's train in these 4 seconds. The latter distance, due to the speed of $60 \frac{\mathrm{km}}{\mathrm{h}}$ of Ulrike's train, is

$$
4 s \cdot \frac{60 \cdot 1000 \mathrm{~m}}{3600 \mathrm{~s}}=\frac{200}{3} \mathrm{~m}
$$

Thus, the oncoming train covers the distance $120 \mathrm{~m}-\frac{200}{3} \mathrm{~m}=\frac{160}{3} \mathrm{~m}$ in 4 seconds; therefore, its speed is uniquely determined by the given information, it is $48 \frac{\mathrm{km}}{\mathrm{h}}$.