How many degrees will the minute hand of a clock move in the same time that the second hand moves through 5400 degrees?

Introduction / Context:
This problem, like an earlier one, compares the movement of the second hand and the minute hand. The second hand is given to move through 5400 degrees, and we are asked how far the minute hand moves in that same period. This is a straightforward proportional reasoning question based on angular speeds of different clock hands.

Given Data / Assumptions:

• The second hand moves 5400 degrees.
• The second hand completes 360 degrees in 60 seconds.
• The minute hand completes 360 degrees in 3600 seconds.
• We must find the angular movement of the minute hand in the same time interval.

Concept / Approach:
First, determine the time taken for the second hand to move 5400 degrees. To do that, we use its known angular speed in degrees per second. Once we know the duration, we use the angular speed of the minute hand to calculate how far it moves in that same number of seconds. This is a classic speed multiplied by time approach, using consistent units.

Step-by-Step Solution:
Step 1: The second hand completes 360 degrees in 60 seconds, so its speed is 360 / 60 = 6 degrees per second. Step 2: Time taken to move 5400 degrees is: time = 5400 / 6 seconds. Step 3: Compute this: 5400 / 6 = 900 seconds. Step 4: The minute hand completes 360 degrees in 3600 seconds, so its speed is 360 / 3600 = 0.1 degrees per second. Step 5: In 900 seconds, the minute hand moves: angle = 0.1 * 900 degrees. Step 6: Calculate the angle: 0.1 * 900 = 90 degrees. Step 7: Therefore, the minute hand moves 90 degrees during the time the second hand moves 5400 degrees.

Verification / Alternative check:
Again, this can be verified using the ratio of speeds. The second hand moves at 6 degrees per second, the minute hand at 0.1 degrees per second. The ratio of their speeds is 6 : 0.1 = 60 : 1. Hence, for every 60 degrees moved by the second hand, the minute hand moves 1 degree. For 5400 degrees of movement by the second hand, the minute hand movement is 5400 / 60 = 90 degrees. This confirms the previous calculation.

Why Other Options Are Wrong:
85 degrees: Close to the correct value but not equal to the exact ratio, so it cannot be correct.

60 degrees: Would correspond to a 90 : 1 speed ratio, which is not the case for these hands.

45 degrees: This is half the correct answer and might result from accidentally dividing by 120 instead of 60.

75 degrees: Does not match the precise 60 : 1 proportion between second hand and minute hand speeds.

Common Pitfalls:
Learners may mistakenly treat the minute hand speed as 6 degrees per minute rather than converting everything into degrees per second. Others may divide by the wrong factor when using the ratio method. Always check the basic angular speeds and ensure that time units match before applying any proportion or calculation.

Final Answer:
The minute hand moves 90 degrees in the time that the second hand moves 5400 degrees.