Special watch

Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?

Result

h₁ = 6:10
h₂ = 9:50

Solution:

$d=\dfrac{ 360 }{ 12 }=30 \ ^\circ \ \\ A=125 \ ^\circ \ \\ B=360 - A=360 - 125=235 \ ^\circ \ \\ \ \\ m_{1}=2 \cdot \ d=2 \cdot \ 30=60 \ ^\circ \ \\ \ \\ h_{1}=(A + m_{1}) / d=(125 + 60) / 30=\dfrac{ 37 }{ 6 }=6.16667=6:10$

$$\begin{gathered} h_2=(B+m_1)\mathrm{/}d=(235+60)\mathrm{/}30\doteq {\displaystyle \frac{59}{6}}\doteq 9.8333=9.83333\doteq 9:50 \\ {h}_2\mathrm{.}\mathrm{.}\mathrm{.}nevyhovuje \end{gathered}$$

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