Three legs journey

A train runs for 3 h at the speed of 40 km/h and then for 4.5 h at the speed of 60 km/h.Thus it covers 3/5th part of the whole distance. It wants to cover the remaining distance in 4 h, find the average speed of the train for remaining distance.

Final Answer:

v₃ =  65 km/h

Step-by-step explanation:

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

Try another example