By how many degrees does the minute hand move in the same time, in which the hour hand move by 18 degree?

Options

A. 168 degree
B. 216 degree
C. 196 degree
D. 276 degree

Explanation

To solve the problem of how many degrees the minute hand moves in the same time that the hour hand moves by 18 degrees, we can follow these steps:

### Step 1: Understand the movement of the hour hand
The hour hand of a clock moves 360 degrees in 12 hours.

### Step 2: Calculate the degrees moved by the hour hand per hour
To find out how many degrees the hour hand moves in one hour, we divide 360 degrees by 12 hours:
\[ \text{Degrees per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour} \]

### Step 3: Calculate the degrees moved by the hour hand per minute
Since there are 60 minutes in an hour, we can find out how many degrees the hour hand moves in one minute by dividing the degrees per hour by 60:
\[ \text{Degrees per minute} = \frac{30 \text{ degrees}}{60 \text{ minutes}} = 0.5 \text{ degrees per minute} \]

### Step 4: Determine the time taken for the hour hand to move 18 degrees
Now, we need to find out how many minutes it takes for the hour hand to move 18 degrees. We can do this by dividing the degrees moved (18 degrees) by the degrees moved per minute (0.5 degrees):
\[ \text{Time in minutes} = \frac{18 \text{ degrees}}{0.5 \text{ degrees per minute}} = 36 \text{ minutes} \]

### Step 5: Calculate the movement of the minute hand in 36 minutes
The minute hand moves 360 degrees in 60 minutes. Therefore, to find out how many degrees it moves in one minute, we divide 360 degrees by 60:
\[ \text{Degrees per minute} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees per minute} \]

Now, we can calculate how far the minute hand moves in 36 minutes:
\[ \text{Degrees moved by minute hand} = 36 \text{ minutes} \times 6 \text{ degrees per minute} = 216 \text{ degrees} \]

### Final Answer
Thus, the minute hand moves **216 degrees** in the same time that the hour hand moves by 18 degrees.

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