Klara

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

Result

t = hh:mm (Correct answer is: 14/13)
s =  6.087 km

Solution:

$s_{1}=s_{2} \ \\ v_{1} \cdot \ (t-13)=v_{2} \cdot \ (t-14) \ \\ \ \\ 5 \cdot \ (x-13)=28 \cdot \ (x-14) \ \\ \ \\ 23x=327 \ \\ \ \\ x=\dfrac{ 327 }{ 23 } \doteq 14.217391 \ \\ \ \\ t=14:13$
$s=5 \cdot \ (x-13)=5 \cdot \ (14.2174-13)=\dfrac{ 140 }{ 23 }=6.087 \ \text{km}$

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