Drivers

Driver Franta and driver Karel are friends. They leave the start-stop both at the same time in the afternoon - at 13.30. When will they meet again if Franta goes around his route in 50 minutes and Karel in 40 minutes?

Result

t = 16:50 hh:mm

Solution:

$$\begin{gathered} 50=2\cdot 5^2 \\ 40=2^3\cdot 5 \\ LCM(50,40)=2^3\cdot 5^2=200 \\ x=LCM(50,40)=200 \\ t=13.50+x\mathrm{/}60=13.50+200\mathrm{/}60={\displaystyle \frac{101}{6}}=16.83333=16:50\text{ hh}:\text{mm} \end{gathered}$$

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