How many degrees will the minute hand of a clock move in the same time that the second hand moves through 4800 degrees?

Introduction / Context:
This question links the motions of the second hand and the minute hand on a clock. Instead of directly using time, it describes the second hand moving through a specific angular distance and asks how far the minute hand moves during exactly the same interval. The problem therefore tests understanding of angular speeds of different hands and proportional reasoning.

Given Data / Assumptions:

• The second hand moves through 4800 degrees.
• The second hand completes 360 degrees in 60 seconds.
• The minute hand completes 360 degrees in 60 minutes, that is, 3600 seconds.
• We must find the angle moved by the minute hand in the same time the second hand uses to move 4800 degrees.

Concept / Approach:
First, we use the angular speed of the second hand to find the time taken for it to move 4800 degrees. Once this time is known, we use the angular speed of the minute hand to compute how far it moves in that same interval. The key is to keep units consistent, typically using seconds for both hands, and then apply simple direct proportion.

Step-by-Step Solution:
Step 1: Calculate the speed of the second hand. It completes 360 degrees in 60 seconds, so its speed is 360 / 60 = 6 degrees per second. Step 2: Time taken by the second hand to move 4800 degrees is: time = 4800 / 6 seconds. Step 3: Compute this value: 4800 / 6 = 800 seconds. Step 4: Now find the angular speed of the minute hand. It completes 360 degrees in 3600 seconds, so its speed is 360 / 3600 = 0.1 degrees per second. Step 5: In the same 800 seconds, the minute hand moves: angle = 0.1 * 800 degrees. Step 6: Multiply to get angle = 80 degrees. Step 7: Therefore, the minute hand moves 80 degrees while the second hand moves 4800 degrees.

Verification / Alternative check:
Another way to see this is as a ratio problem. The speeds of the second and minute hands are 6 degrees per second and 0.1 degrees per second respectively. The ratio of their speeds is 6 : 0.1 = 60 : 1. So, when the second hand moves 4800 degrees, the minute hand moves 4800 / 60 = 80 degrees. This shortcut matches the detailed calculation, confirming the result.

Why Other Options Are Wrong:
160 degrees: This is double the correct value and would result from dividing by 30 instead of 60.

140 degrees: Not supported by any correct ratio of speeds for the two hands.

135 degrees: This is a common approximate value in some angle problems but does not fit the exact proportion here.

60 degrees: This would correspond to a 1:80 ratio instead of 1:60, which is not correct for these hand speeds.

Common Pitfalls:
Typical errors include mixing up minutes and seconds or assigning incorrect speeds to the hands. Some students incorrectly assume that the minute hand moves 6 degrees per minute and then forget to convert time units consistently. Always convert both motions into the same time unit, preferably seconds, and then apply direct proportionality using the correct angular speeds.

Final Answer:
In the given interval, the minute hand moves 80 degrees.