A medium question on clocks and time for P3–P4, with a step-by-step solution, diagrams and the answer. Every year of the Hua Xia Cup has clock questions, from time passed in P1 to the angle between the hands in P6.
The question
At 3:16 pm, Ming, doing homework at home, looks up at the wall clock.
What is the smaller angle between the hour hand and the minute hand?
Show the hints (2)
💡Hint 1: The minute hand goes round in an hour, the hour hand in twelve hours; a full turn is 360 degrees. How far does each move per minute, per hour?
💡Hint 2: The hour hand is not exactly on 3: in these 16 minutes it has moved on too, one degree every two minutes.
Worked solution
Have a go first, then read the solution step by step.
1.The minute hand moves 360 ÷ 60 = 6 degrees a minute. At 16 minutes past, it is 6 × 16 = 96 degrees round from 12.
2.The hour hand moves 360 ÷ 12 = 30 degrees an hour, which is 1 degree every 2 minutes. At 3:16 it is 30 × 3 + 16 ÷ 2 = 98 degrees round from 12.
3.The hands are 98 − 96 = 2 degrees apart.
⚠️Common mistake: leaving the hour hand on 3, which gives 6 degrees.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download