Mountain and hiker

The hiker set out on a hike at 5 km/h. After 30 minutes, a cyclist on a mountain bike set off on the same route at 20 km/h. After how many minutes will the cyclist overtake the hiker?

Final Answer:

t =  10 min

Step-by-step explanation:

$$\begin{gathered} v_1=5\text{km/h} \\ {v}_2=20\text{km/h} \\ \Delta =30\text{min}\to \text{h}=30:60\text{h}=0.5\text{h} \\ {s}_1=s_2 \\ {v}_1\cdot (x+\Delta )=v_2\cdot x \\ 5\cdot (x+0.5)=20\cdot x \\ 15x=2.5 \\ x=\frac{2.5}{15}=0.16666667 \\ x=\frac{1}{6}\doteq 0.166667 \\ t=x\to \text{min}=x\cdot 60\text{min}=0.1667\cdot 60\text{min}=10\text{min}=10\text{min} \end{gathered}$$

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