Hoverboard

Adam lives in Podhradí, and his friend Marcel lives in Lhota. Lhota is 6 km from Podhradí. Adam travels the same distance on a hoverboard in 20 minutes as Marcel does in 25 minutes. They leave home simultaneously, drive towards each other, and meet in precisely 15 minutes. Calculate how fast Adam is going and how fast Marcel is driving.

Final Answer:

v₁ =  13.3333 km/h
v₂ =  10.6667 km/h

Step-by-step explanation:

$$\begin{gathered} s=6\text{km} \\ t=15\text{min}\to \text{h}=15:60\text{h}=0.25\text{h} \\ v=s/t=6/0.25=24\text{km/h} \\ v=v_1+v_2 \\ {t}_1=20\text{min}\to \text{h}=20:60\text{h}=0.33333\text{h} \\ {t}_2=25\text{min}\to \text{h}=25:60\text{h}=0.41667\text{h} \\ x=v_1\cdot t_1=v_2\cdot t_2 \\ v=v_1+v_2 \\ v=v_1+v_1\cdot t_1/t_2 \\ {t}_2\cdot v=t_2\cdot v_1+v_1\cdot t_1 \\ 0.41666666666667\cdot 24=0.41666666666667\cdot v_1+v_1\cdot 0.33333333333333 \\ 0.75v_1=10 \\ {v}_1=\frac{10}{0.75}=13.33333333 \\ {v}_1=\frac{40}{3}\doteq 13.333333=13.3333\text{km/h} \end{gathered}$$

$v_2=v-v_1=24-13.3333=10.6667\text{km/h}$

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