Bus catching calculation

Mr. Pozdechodim missed the bus at 10.05. At 10.10, he passed Jindra. The bus travels at an average speed of 60 km/h and Jindra at 80 km/h. Will they catch the bus, which is 20 km from the next stop?

Final Answer:

s =  20 km

Step-by-step explanation:

$$\begin{gathered} v_1=60\text{km/h} \\ {v}_2=80\text{km/h} \\ \Delta =5\text{min}\to \text{h}=5:60\text{h}=0.08333\text{h} \\ s=v_1\cdot t \\ s=v_2\cdot (t-\Delta ) \\ {v}_1\cdot t=v_2\cdot (t-\Delta ) \\ 60\cdot t=80\cdot (t-0.083333333333333) \\ 20t=6.666667 \\ t=\frac{6.66666667}{20}=0.33333333 \\ t=\frac{1}{3}\doteq 0.333333 \\ s=v_1\cdot t=60\cdot 0.3333=20\text{km} \end{gathered}$$

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