Cyclist pursuit

The pedestrian walks at a speed of 4.3 km/h. In 1 hour and 10 minutes, a cyclist followed him at an average 18 km/h speed. How many minutes will a cyclist reach a pedestrian, and how many kilometers will he travel?

Final Answer:

t =  21.9708 min
s =  6.5912 km

Step-by-step explanation:

$$\begin{gathered} v_1=4.3\text{km/h} \\ {v}_2=18\text{km/h} \\ \Delta t=1:10=1hr10min=1+\frac{10}{60}=1.1667hr\doteq 1.1667 \\ {v}_1\cdot (x+\Delta t)=v_2\cdot x \\ 4.3\cdot (x+1.1666666666667)=18\cdot x \\ 13.7x=5.016667 \\ x=\frac{5.01666667}{13.7}=0.36618005 \\ x=\frac{301}{822}\doteq 0.36618 \\ t=x\to \text{min}=x\cdot 60\text{min}=0.3662\cdot 60\text{min}=21.971\text{min}=21.9708\text{min} \end{gathered}$$

$s=v_2\cdot x=18\cdot 0.3662=6.5912\text{km}$

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