Train pursuit meeting

A train travels at a speed of 50 km/h from city A. In 15 minutes, a second train follows him at 20 m/s. We are sitting on the first train. When will the second train catch up with the first?

Final Answer:

t₂ =  34.0909 min

Step-by-step explanation:

$$\begin{gathered} v_1=50\text{km/h}\to \text{m/s}=50:3.6\text{m/s}=13.88889\text{m/s} \\ {t}_1=15\text{min}\to \text{s}=15\cdot 60\text{s}=900\text{s} \\ {v}_2=20\text{m/s} \\ {s}_1=s_2 \\ {v}_1\cdot (t+t_1)=v_2\cdot t \\ 13.888888888889\cdot (t+900)=20\cdot t \\ 6.111111t=12500 \\ t=\frac{12500}{6.11111111}=2045.45454545 \\ t=\frac{22500}{11}\doteq 2045.454545 \\ {t}_2=t\to \text{min}=t:60\text{min}=2045.4545:60\text{min}=34.091\text{min}=34.0909\text{min} \end{gathered}$$

Try another example