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:

$d = \dfrac{ 360 }{ 12 } = 30 \ ^\circ \ \\ A = 125 \ ^\circ \ \\ B = 360 - A = 360 - 125 = 235 \ ^\circ \ \\ \ \\ m_{ 1 } = 2 \cdot \ d = 2 \cdot \ 30 = 60 \ ^\circ \ \\ \ \\ h_{ 1 } = (A + m_{ 1 }) / d = (125 + 60) / 30 = \dfrac{ 37 }{ 6 } \doteq 6.1667 = 6.16667 = 6:10$

$h_{ 2 } = (B+m_{ 1 }) / d = (235+60) / 30 = \dfrac{ 59 }{ 6 } \doteq 9.8333= 9.83333 = 9:50 \ \\ h_{ 2 } ... nevyhovuje$

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