A train 3

A train takes 3 hours to go from one station to another station. If its speed is decreased by 12 km/h then the journey time will increase by 45 min. What is the distance between the two stations?

Final Answer:

s =  180 km

Step-by-step explanation:

$$\begin{gathered} t_1=3\text{h} \\ \Delta v=12\text{km/h} \\ {t}_2=t_1+\frac{45}{60}=3+\frac{45}{60}=\frac{3\cdot 60}{60}+\frac{45}{60}=\frac{180}{60}+\frac{45}{60}=\frac{180+45}{60}=\frac{225}{60}=\frac{15}{4}=3.75\text{h} \\ s=v_1\cdot t_1=v_2\cdot t_2 \\ {v}_1\cdot t_1=(v_1-\Delta v)\cdot t_2 \\ {v}_1\cdot 3=(v_1-12)\cdot 3.75 \\ 0.75v_1=45 \\ {v}_1=\frac{45}{0.75}=60 \\ {v}_1=60 \\ {v}_2=v_1-\Delta v=60-12=48\text{km/h} \\ s=v_1\cdot t_1=60\cdot 3=180\text{km} \end{gathered}$$

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