- A Boat has to cover 13 km in ds and speed of the boat in still water is 14km/H. After travelling for 30 min, the speed of the stream is decreased to 4km/H and the or remaining distance in Covered in 10 min. Find the Pultial speed of stream?

To solve this problem, let's break it down into parts:

### 1. **Distance covered in the first part:**
   - Speed of the boat in still water \( V_b = 14 \) km/h.
   - Let the initial speed of the stream be \( V_s \) km/h.
   - Speed of the boat downstream \( = V_b + V_s \).
   - Time taken in the first part \( t_1 = 30 \) minutes \( = \frac{30}{60} = 0.5 \) hours.
   - Distance covered in the first part \( d_1 \) is:
     \[
     d_1 = (V_b + V_s) \times t_1
     \]

### 2. **Distance covered in the second part:**
   - After 30 minutes, the speed of the stream decreases to 4 km/h.
   - New speed of the boat downstream \( = V_b + 4 \) km/h.
   - Time taken in the second part \( t_2 = 10 \) minutes \( = \frac{10}{60} = \frac{1}{6} \) hours.
   - Distance covered in the second part \( d_2 \) is:
     \[
     d_2 = (V_b + 4) \times \frac{1}{6}
     \]

### 3. **Total distance covered:**
   - Total distance \( D = 13 \) km.
   - \( D = d_1 + d_2 \):
     \[
     13 = (V_b + V_s) \times 0.5 + \left(V_b + 4\right) \times \frac{1}{6}
     \]

### 4. **Substitute the known values:**
   \[
   13 = (14 + V_s) \times 0.5 + \left(14 + 4\right) \times \frac{1}{6}
   \]
   \[
   13 = \frac{14 + V_s}{2} + \frac{18}{6}
   \]
   \[
   13 = \frac{14 + V_s}{2} + 3
   \]

### 5. **Solve for \( V_s \):**
   \[
   13 - 3 = \frac{14 + V_s}{2}
   \]
   \[
   10 = \frac{14 + V_s}{2}
   \]
   \[
   20 = 14 + V_s
   \]
   \[
   V_s = 20 - 14 = 6 \text{ km/h}
   \]

### Final Answer:
The initial speed of the stream \( V_s \) was **6 km/h**.

Would you like a detailed explanation of any step or have any questions? 

Here are some related questions to expand your understanding:

1. How would the problem change if the boat was traveling upstream instead?
2. What if the boat had a different speed in still water?
3. How would the calculation differ if the stream's speed increased instead of decreasing?
4. What if the time taken in the second part was longer?
5. How would the total time taken affect the speed of the stream?

**Tip:** Always double-check the units when converting time to ensure consistency in your calculations.

Explore how to solve a problem involving a boat's journey covering 13 km with varying stream speeds. Understand the calculation steps and formula applications with a detailed solution. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation