Three journeys

If a person covers three equal distances at the speed of 30 km/h, 15 km/h and 10 km/h respectively, then find out the average speed during the whole journey.

Correct answer:

v =  15 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=30\text{km/h} \\ {v}_2=15\text{km/h} \\ {v}_3=10\text{km/h} \\ {s}_1=s_2=s_3=s \\ {t}_1=s/v_1 \\ {t}_2=s/v_2 \\ {t}_3=s/v_3 \\ v=\frac{3\cdot s}{t_1+t_2+t_3} \\ v=\frac{3\cdot s}{s/v_1+s/v_2+s/v_3} \\ v=\frac{3}{1/v_1+1/v_2+1/v_3}=\frac{3}{1/30+1/15+1/10}=15\text{km/h} \end{gathered}$$

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