One-third 18

One-third of a certain journey was covered at the speed of 20 km/h, one-fourth at 30 km/h, and the rest at the speed of 50 km/h. Find the average speed of the whole journey.

Correct answer:

v =  30 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=20\text{km/h} \\ {v}_2=30\text{km/h} \\ {v}_3=50\text{km/h} \\ {s}_1=s/3 \\ {s}_2=s/4 \\ {s}_3=s-s_1-s_2=fr(,5,12)s \\ v=\frac{s}{t}=\frac{s}{s_1/v_1+s_2/v_2+s_3/v_3} \\ v=\frac{s}{(s/3)/v_1+(s/4)/v_2+(5/12s)/v_3} \\ v=\frac{1}{\frac{1}{3\cdot v_1}+\frac{1}{4\cdot v_2}+\frac{5}{12\cdot v_3}}=\frac{1}{\frac{1}{3\cdot 20}+\frac{1}{4\cdot 30}+\frac{5}{12\cdot 50}}=30\text{km/h} \end{gathered}$$

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