Between 5 and 6 o'clock the hands of a clock are at right angles twice. At what time does this happen the SECOND time?

10\frac{10}{11}

minutes past 5Correct answerYour answer

27\frac{3}{11}

minutes past 5Correct answerYour answer

40

minutes past 5Correct answerYour answer

43\frac{7}{11}

minutes past 5Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

At 5:00 the minute hand is $150^\circ$ behind the hour hand. The second right angle comes after the minute hand has passed the hour hand and is $90^\circ$ ahead of it.
So the minute hand must gain $150 + 90 = 240^\circ$ .
Time $= 240 \div 5.5 = \frac{480}{11} = 43\frac{7}{11}$ minutes past 5.

Worth noting

$10\frac{10}{11}$ is the FIRST right angle (gain of $60^\circ$ ). $27\frac{3}{11}$ is when the hands coincide. 40 ignores the hour hand's movement.

Ten questions from Calendars and Clocks, at your own pace.

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