29 boys are standing in a line such that distance between any two consecutive boys is same. A teachr takes 7 seconds to reach from first boy to 15th boy. How much more time (in seconds) will he take to reach the 22nd boy?

Options

A. `2.5`
B. 3
C. `3.5`
D. 4

Answer

To solve the problem step by step, we will analyze the information given and calculate the time taken by the teacher to reach the 22nd boy from the 15th boy.

### Step 1: Understand the distance between the boys
There are 29 boys standing in a line, and the distance between any two consecutive boys is the same. Let's denote the distance between two consecutive boys as \( x \).

### Step 2: Calculate the distance from the 1st boy to the 15th boy
The distance from the 1st boy to the 15th boy can be calculated as follows:
- The number of gaps between the 1st boy and the 15th boy is \( 15 - 1 = 14 \).
- Therefore, the distance from the 1st boy to the 15th boy is \( 14x \).

### Step 3: Determine the time taken to reach from the 1st boy to the 15th boy
According to the problem, the teacher takes 7 seconds to reach from the 1st boy to the 15th boy.

### Step 4: Calculate the velocity of the teacher
The velocity \( v \) of the teacher can be calculated using the formula:
\[ v = \frac{\text{Distance}}{\text{Time}} = \frac{14x}{7} = 2x \text{ (units per second)} \]

### Step 5: Calculate the distance from the 15th boy to the 22nd boy
Now, we need to find the distance from the 15th boy to the 22nd boy:
- The number of gaps between the 15th boy and the 22nd boy is \( 22 - 15 = 7 \).
- Therefore, the distance from the 15th boy to the 22nd boy is \( 7x \).

### Step 6: Calculate the time taken to reach from the 15th boy to the 22nd boy
Using the velocity calculated earlier, we can find the time \( t \) taken to reach from the 15th boy to the 22nd boy:
\[ t = \frac{\text{Distance}}{\text{Velocity}} = \frac{7x}{2x} = \frac{7}{2} = 3.5 \text{ seconds} \]

### Step 7: Calculate the additional time taken
Since the question asks for how much more time the teacher will take to reach the 22nd boy from the 15th boy, the answer is:
\[ \text{Additional time} = 3.5 \text{ seconds} \]

### Final Answer
The teacher will take **3.5 seconds** more to reach the 22nd boy from the 15th boy.

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