The tourist

The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up, and how many kilometers will he go?

Correct answer:

t =  10 min
s =  3.3333 km

Step-by-step explanation:

$$\begin{gathered} 5\cdot (t/60+30/60)=s \\ s=20\cdot t/60 \\ 60s-5t=150 \\ 60s-20t=0 \\ Row2-Row1\to Row2 \\ 60s-5t=150 \\ -15t=-150 \\ t=\frac{-150}{-15}=10 \\ s=\frac{150+5t}{60}=\frac{150+5\cdot 10}{60}=3.33333333 \\ s=\frac{10}{3}\doteq 3.333333 \\ t=10=10\text{min} \end{gathered}$$

$s=3.3333=3.3333\text{km}$

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