## Task 2 - 030912

Wolfgang is on a train, whose own speed he has measured at $60 \mathrm{~km} / \mathrm{h}$. He wants to determine the speed of an oncoming double-decker articulated train. He knows that this double-decker articulated train, including the locomotive, is approximately $120 \mathrm{~m}$ long, and he times the duration it takes for the train to pass by, which is exactly 3.0 s.

At what speed is the oncoming train traveling?
The two trains are moving towards each other. Specifically, the point where Wolfgang performs his measurements and the end of the oncoming train are moving towards each other and reduce their distance by \( s = s_{W} + s_{G} = 120 \, \text{m} \) in the time \( t = 3.0 \, \text{s} \), where \( s_{W} \) describes the portion of the distance covered by Wolfgang's train, and \( s_{G} \) stands for the distance covered by the oncoming train.

Furthermore, the speed \( v_{W} \) at which Wolfgang's train is traveling is known: \( v_{W} = 60 \, \text{km/h} \). The speed \( v_{G} \) of the oncoming train can be calculated as follows:

\[
v_{G} = \frac{s_{G}}{t} = \frac{s - s_{W}}{t} = \frac{s - v_{W} t}{t} = \frac{s}{t} - v_{W} = \frac{120 \, \text{m}}{3.0 \, \text{s}} - 60 \, \text{km/h} = 84 \, \text{km/h}
\]