Multiple choice

At what time between 1 and 2 o' clock will the hands of a watch makes an angle of 180°

  1. 35(5/11) min. past 1

  2. 40 min. past 1

  3. 50(4/11) min. past

  4. 38(2/11) min. past 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At 1 o'clock, the minute hand is at 12 and the hour hand is at 1. To be 180 degrees apart, the minute hand must be at 7 (35 minutes past). The relative speed is 5.5 degrees per minute. Time = 35 * (12/11) = 420/11 = 38 2/11 minutes past 1.

AI explanation

Using the formula for finding the time when the hands form a specific angle, M equals 2 divided by 11 times the quantity 30 times H plus or minus the angle, where H is the starting hour. Substituting H as 1 and the angle as 180 degrees gives M equals 2 divided by 11 times the quantity 30 plus 180. This simplifies to 420 divided by 11, which results in the time being 38 and 2 divided by 11 minutes past 1.

Keep practicing — related questions