50 trees are standing in a line such that distance between any two consecutive trees is same. A car takes 18 seconds to travel from 13th tree to 34th tree. How much time (in seconds) will it take to reach from the first tree to the 50th tree?

Options

A. 42
B. `42.85`
C. 45
D. 49

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Identify the distance between trees
Let the distance between any two consecutive trees be \( x \) meters.

### Step 2: Calculate the distance from the 13th tree to the 34th tree
The number of trees from the 13th tree to the 34th tree is:
\[ 34 - 13 = 21 \text{ trees} \]
Since the distance between each tree is \( x \), the total distance covered from the 13th tree to the 34th tree is:
\[ 21x \text{ meters} \]

### Step 3: Calculate the speed of the car
The car takes 18 seconds to travel from the 13th tree to the 34th tree. Therefore, the speed \( v \) of the car can be calculated using the formula:
\[ v = \frac{\text{Distance}}{\text{Time}} = \frac{21x}{18} \]
Simplifying this gives:
\[ v = \frac{21}{18}x = \frac{7}{6}x \text{ meters per second} \]

### Step 4: Calculate the distance from the 1st tree to the 50th tree
The number of trees from the 1st tree to the 50th tree is:
\[ 50 - 1 = 49 \text{ trees} \]
Thus, the total distance from the 1st tree to the 50th tree is:
\[ 49x \text{ meters} \]

### Step 5: Calculate the time taken to travel from the 1st tree to the 50th tree
Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values:
\[ \text{Time} = \frac{49x}{\frac{7}{6}x} \]
Here, \( x \) cancels out:
\[ \text{Time} = 49 \cdot \frac{6}{7} \]
Calculating this gives:
\[ \text{Time} = \frac{294}{7} = 42 \text{ seconds} \]

### Final Answer
The time taken to reach from the 1st tree to the 50th tree is **42 seconds**.

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