Motion

If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving the train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure.
How far is the train station?

Correct answer:

s =  7.003 km

Step-by-step explanation:

$$\begin{gathered} v_1=3.7\text{km/h} \\ {v}_2=27\text{km/h} \\ {t}_1=(x+42)/60\text{h} \\ {t}_2=(x-56)/60\text{h} \\ s=v_1\cdot t_1=v_2\cdot t_2 \\ {v}_1(x+42)=v_2(x-56) \\ x=(v_1\cdot 42+v_2\cdot 56)/(v_2-v_1)=(3.7\cdot 42+27\cdot 56)/(27-3.7)\doteq 71.5622\text{min} \\ {t}_1=(x+42)/60=(71.5622+42)/60=\frac{441}{233}\doteq 1.8927\text{h} \\ {t}_2=(x-56)/60=(71.5622-56)/60\doteq 0.2594\text{h} \\ s=s_1=s_2 \\ {s}_1=v_1\cdot t_1=3.7\cdot 1.8927\doteq 7.003\text{km} \\ s=v_2\cdot t_2=27\cdot 0.2594=7.003\text{km} \end{gathered}$$

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