At 4:24 pm, how many degrees has the hour hand of a clock moved from its position at noon?
(1) 132°
(2) 135°
(3) 140°
(4) 145°
Answer (2)
The hour hand of a clock has moved 132 degrees from its position at noon to 4:24 PM. This is calculated by converting the elapsed time into hours and determining how many degrees the clock hand moves per hour. The correct option is (1) 132°.
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To determine how many degrees the hour hand has moved from its position at noon to 4:24 PM, we follow these calculations step by step:
Determine the total hours and minutes past noon:
From 12:00 PM to 4:24 PM, there are 4 hours and 24 minutes.
Calculate the degrees moved per hour:
The hour hand moves 360 degrees in 12 hours (a full circle of the clock).
This means it moves 12 360 = 30 degrees per hour.
Calculate the degrees moved in 4 hours:
For 4 hours, the degrees moved by the hour hand is 4 × 30 = 120 degrees.
Calculate the additional degrees moved in 24 minutes:
Since the hour hand moves 30 degrees in 60 minutes, in 1 minute, it moves 60 30 = 0.5 degrees.
For 24 minutes, the degrees moved is 24 × 0.5 = 12 degrees.
Add the degrees moved in hours and minutes:
Total degrees from noon until 4:24 PM is 120 + 12 = 132 degrees.
Therefore, the hour hand has moved 132 degrees from its position at noon to 4:24 PM.
The correct answer is option (1) 132°.
