Cyclists and walkers

A group of tourists started at 8:00 at a speed of 4 km/h walk. At half-past ten, another group started on a bike and caught up with a group of tourists at 10:50. What was the average speed of cyclists?

Correct answer:

v₂ =  8.5 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=4\text{km/h} \\ {t}_3=10:50=10hr50min=10+\frac{50}{60}=10.8333hr\doteq 10.8333 \\ {t}_1=t_3-8.00=\frac{65}{6}-8.00=\frac{17}{6}\doteq 2.8333\text{h} \\ {t}_2=t_3-(9+30/60)=\frac{65}{6}-(9+30/60)=\frac{4}{3}\doteq 1.3333\text{h} \\ {s}_1=s_2 \\ {v}_1\cdot t_1=v_2\cdot t_2 \\ {v}_2=v_1\cdot \frac{t_1}{t_2}=4\cdot \frac{\frac{17}{6}}{\frac{4}{3}}=\frac{17}{2}\text{km/h}=8.5\text{km/h} \end{gathered}$$

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