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 1st tree to 50th tree?

Options

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

Answer

To solve the problem step by step, we need to determine the time it takes for the car to travel from the 1st tree to the 50th tree based on the information given about the travel time between the 13th and 34th trees.

### Step 1: Identify the number of trees and distances
We know that there are 50 trees standing in a line, and the distance between any two consecutive trees is the same.

### Step 2: Calculate the number of trees between the 13th and 34th trees
To find the number of trees between the 13th and 34th trees, we can calculate:
- The number of trees from the 13th to the 34th tree is given by:
\[ 34 - 13 = 21 \text{ trees} \]
However, since we are counting the trees, we should consider the distance traveled which is between the 13th tree and the 34th tree, meaning there are 21 gaps between them.

### Step 3: Calculate the time taken per gap
The car takes 18 seconds to travel from the 13th tree to the 34th tree, which covers 21 gaps. Therefore, the time taken for each gap is:
\[ \text{Time per gap} = \frac{18 \text{ seconds}}{21 \text{ gaps}} = \frac{6}{7} \text{ seconds per gap} \]

### Step 4: Calculate the total number of gaps from the 1st tree to the 50th tree
To find the total number of gaps from the 1st tree to the 50th tree, we calculate:
- The number of gaps between the 1st and 50th trees is:
\[ 50 - 1 = 49 \text{ gaps} \]

### Step 5: Calculate the total time to travel from the 1st tree to the 50th tree
Now, we can find the total time taken to travel from the 1st tree to the 50th tree by multiplying the number of gaps by the time taken per gap:
\[ \text{Total time} = 49 \text{ gaps} \times \frac{6}{7} \text{ seconds per gap} = \frac{294}{7} = 42 \text{ seconds} \]

### Conclusion
Thus, the time taken for the car to travel from the 1st tree to the 50th tree is **42 seconds**.

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