Clocks

Read the formula sheet first, then work through the 5 questions below. Each answer comes with a step-by-step solution — read it even when you get the question right, the shortcut is often faster than your method.

Formula sheet

• Minute hand moves 6° per minute; hour hand 0.5° per minute → relative 5.5° per minute.
• Angle at h hours m minutes = |30h − 5.5m| (take 360 − angle if > 180).
• Hands coincide 11 times in 12 hours (22 times in 24 h); at right angles 22 times in 12 h; opposite 11 times in 12 h.
• Hands overlap every 65 5/11 minutes. Faulty (slow/fast) clock: compare the time it shows with the true time elapsed and use the ratio.
• For hands to be together after h o’clock: (60h/11) minutes past h.
• Minute-spaces: the dial has 60; the minute hand gains 55 minute-spaces on the hour hand every hour.

Practice

Pick an answer to see whether it is right and the worked solution. Your score is saved when you finish the set.