Pedestrians 40811

From Tatranská Lomnica to Ždiar, 40 km apart, two groups of tourists went opposite each other. Pedestrians left Tatranská Lomnica at 9:00 AM at an average speed of 4 km/h. Cyclists from Ždiar at 9:30 at an average speed of 15 km/h.
When will they meet?
At what distance from the starting point will they compete?

Result

t = 11:30
s₁ =  10 km
s₂ =  30 km

Step-by-step explanation:

$$\begin{gathered} s=40\text{km} \\ {v}_1=4\text{km/h} \\ {v}_2=15\text{km/h} \\ s=v_1\cdot (x-9.00)+v_2\cdot (x-9.5) \\ 40=4\cdot (x-9.00)+15\cdot (x-9.5) \\ 19x=218.5 \\ x=\frac{218.5}{19}=11.5 \\ x=\frac{23}{2}=11.5 \\ t=x=11.5=11:30 \end{gathered}$$

$s_1=v_1\cdot (x-9.00)=4\cdot (11.5-9.00)=10\text{km}$

$s_2=v_2\cdot (x-9.50)=15\cdot (11.5-9.50)=30\text{km}$

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