Average speed

A car traveled from city A to city B at a speed of 40 km/h, then from B to C at 60 km/h, and finally from C to D at 50 km/h. Calculate the car's average speed over the entire route from A to D if the distance from A to B is 20% of the total distance and from B to C is 30% of the total distance.

Final Answer:

v =  51 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=40\text{km/h} \\ {v}_2=60\text{km/h} \\ {v}_3=50\text{km/h} \\ {p}_1=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ {p}_2=30\%=\frac{30}{100}=\frac{3}{10}=0.3 \\ {p}_3=1-p_1-p_2=1-0.2-0.3=\frac{1}{2}=0.5 \\ v=v_1\cdot p_1+v_2\cdot p_2+v_3\cdot p_3=40\cdot 0.2+60\cdot 0.3+50\cdot 0.5=51\text{km/h} \end{gathered}$$

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