At what time between 4 o'clock and 5 o'clock are the hands of a clock together?

18\frac{6}{13}

minutes past 4Correct answerYour answer

20

minutes past 4Correct answerYour answer

21\frac{9}{11}

minutes past 4Correct answerYour answer

24

minutes past 4Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

At 4:00 the minute hand is $120^\circ$ behind the hour hand.
The minute hand gains $6 - 0.5 = 5.5^\circ$ per minute on the hour hand.
Time to close the gap $= 120 \div 5.5 = \frac{240}{11} = 21\frac{9}{11}$ minutes, so $21\frac{9}{11}$ minutes past 4.

Worth noting

20 minutes pretends the hour hand stands still $(120 \div 6)$ . $18\frac{6}{13}$ adds the speeds $(6 + 0.5)$ instead of subtracting them, and 24 divides by 5.

Concept: Hands coinciding: gap ÷ relative speed
Typical timeTypical: 75 s
Your timeYours: —

The rule this testsAngles between the hands

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

At what time between 4 o'clock and 5 o'clock are the hands of a clock together?

Explanation