Three legs journey

A train runs for 3 hours at 40 km/h and then for 4.5 hours at 60 km/h, covering 3/5 of the total distance. It needs to cover the remaining distance in 4 hours. Find the average speed required for the remaining distance.

Final Answer:

v₃ =  65 km/h

Step-by-step explanation:

$$\begin{gathered} t_1=3\text{h} \\ {v}_1=40\text{km/h} \\ {t}_2=4.5\text{h} \\ {v}_2=60\text{km/h} \\ {s}_{12}=v_1\cdot t_1+v_2\cdot t_2=40\cdot 3+60\cdot 4.5=390\text{km} \\ {s}_{12}=\frac{3}{5}\cdot s \\ s=\frac{5}{3}\cdot s_{12}=\frac{5}{3}\cdot 390=\frac{5\cdot 390}{3}=\frac{1950}{3}=650\text{km} \\ {s}_3=s-s_{12}=650-390=260\text{km} \\ {t}_3=4\text{h} \\ {v}_3=\frac{s_3}{t_3}=\frac{260}{4}=65\text{km/h} \end{gathered}$$

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