Two-thirds 80635

The car traveled the first third of the track with a constant speed of v1, the next two-thirds of the way at a constant speed of v2=72km/h, and the average speed of v=36km/h. Find v1.

Correct answer:

v₁ =  18 km/h

Step-by-step explanation:

$$\begin{gathered} s_1=1/3\cdot s\text{km} \\ {s}_2=2/3\cdot s\text{km} \\ {v}_2=72\text{km/h} \\ v=36\text{km/h} \\ t=s/v \\ {t}_2=s_2/v_2 \\ {t}_1=t-t_2 \\ {v}_1=s_1/t_1 \\ {v}_1=1/3\cdot s/(s/v-s_2/v_2) \\ {v}_1=1/3\cdot s/(s/v-2/3\cdot s/v_2) \\ {v}_1=1/3/(1/v-2/3/v_2) \\ {v}_1=\frac{1}{3}/(1/v-\frac{2}{3}/v_2)=\frac{1}{3}/(1/36-\frac{2}{3}/72)=18\text{km/h} \end{gathered}$$

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