Between 8 and 9 o'clock the angle between the hands is 50° twice. At what time is it 50° for the second time?

34\frac{6}{11}

minutes past 8Correct answerYour answer

43\frac{7}{11}

minutes past 8Correct answerYour answer

48\frac{1}{3}

minutes past 8Correct answerYour answer

52\frac{8}{11}

minutes past 8Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

At 8:00 the minute hand is $240^\circ$ behind the hour hand.
The second time, the minute hand has passed the hour hand and is $50^\circ$ ahead: it has gained $240 + 50 = 290^\circ$ .
Time $= 290 \div 5.5 = \frac{580}{11} = 52\frac{8}{11}$ minutes past 8.

Worth noting

$34\frac{6}{11}$ is the first time (gain of $190^\circ$ ). $43\frac{7}{11}$ is when the hands coincide. $48\frac{1}{3}$ divides by 6 and ignores the hour hand.

Concept: Time for a given angle between the hands
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsAngles between the hands

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

Between 8 and 9 o'clock the angle between the hands is 50° twice. At what time is it 50° for the second time?

Explanation