Find all integers $n$ such that when the clock strikes $n$ o'clock, the acute angle between the hour and minute hands is $60^{\circ}$. Enter your answer as a comma-separated list.

qwertyytrewq Feb 5, 2021

#1**+3 **

I belive the answer is 2, 10 and here is the ex

At $n$ o'clock, the minute hand is pointing straight up toward $12$. The hour hand must be $60^{\circ}$ away, either clockwise or counter-clockwise. Since $60^{\circ}$ is $\dfrac{1}{6}$ of a rotation and each full rotation of the hour hand lasts $12$ hours, the hour hand must be pointing $2$ hours in either direction from $12$. The possible times are $\boxed{2{:}00\text{ and }10{:}00}$.

AnswerMachine Feb 5, 2021

#1**+3 **

Best Answer

I belive the answer is 2, 10 and here is the ex

At $n$ o'clock, the minute hand is pointing straight up toward $12$. The hour hand must be $60^{\circ}$ away, either clockwise or counter-clockwise. Since $60^{\circ}$ is $\dfrac{1}{6}$ of a rotation and each full rotation of the hour hand lasts $12$ hours, the hour hand must be pointing $2$ hours in either direction from $12$. The possible times are $\boxed{2{:}00\text{ and }10{:}00}$.

AnswerMachine Feb 5, 2021