Klara

Klara and Jitka went on a hiking trip at 13 o'clock at a speed of 5km/h. At 14 o'clock, Thomas rode on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road did Thomas catch the two girls?

Correct answer:

t = hh:mm 14:13
s =  6.087 km

Step-by-step explanation:

$$\begin{gathered} v_1=5{\text{km/h}}_2 \\ {v}_2=28\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot (t-13)=v_2\cdot (t-14) \\ {v}_1\cdot (x-13)=v_2\cdot (x-14) \\ 5\cdot (x-13)=28\cdot (x-14) \\ 23x=327 \\ x=\frac{327}{23}=14.2173913 \\ x=\frac{327}{23}\doteq 14.217391 \\ t=14:13 \end{gathered}$$

$s=v_1\cdot (x-13)=5\cdot (14.2174-13)=6.087\text{km}$

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