Two friends A and B, on their last day in college, decided to meet after 20 years on a river. A had to sail 42 km to the meeting place and B had to sail 250/7 % less. To arrive at the meeting place at the same time as his friend B, A started at the same time as B and sailed with the speed exceeding by 5 km/h the speed of B. Find the speed of A:

Answer

To solve the problem step by step, we need to find the speed of friend A. Let's break down the information given in the question:

1. **Distances to Meeting Place**:
- Distance A has to sail = 42 km
- Distance B has to sail = 250/7 % less than A's distance.

2. **Calculating B's Distance**:
- First, we need to find out how much distance B has to sail.
- 250/7 % of A's distance = (250/7) / 100 * 42 = (250 * 42) / (7 * 100) = 1050 / 700 = 15 km.
- Therefore, B's distance = 42 km - 15 km = 27 km.

3. **Speed Relationship**:
- Let the speed of B be \( v \) km/h.
- Then, the speed of A = \( v + 5 \) km/h.

4. **Time Taken to Reach the Meeting Place**:
- Time taken by A = Distance / Speed = \( 42 / (v + 5) \) hours.
- Time taken by B = Distance / Speed = \( 27 / v \) hours.

5. **Setting Up the Equation**:
- Since both friends arrive at the meeting place at the same time, we can set the times equal to each other:
\[ \frac{42}{v + 5} = \frac{27}{v} \]

6. **Cross Multiplying**:
- Cross-multiply to eliminate the fractions:
\[ 42v = 27(v + 5) \]

7. **Expanding and Rearranging**:
- Expanding the right side:
\[ 42v = 27v + 135 \]
- Rearranging gives:
\[ 42v - 27v = 135 \]
\[ 15v = 135 \]

8. **Solving for v**:
- Divide both sides by 15:
\[ v = \frac{135}{15} = 9 \text{ km/h} \]

9. **Finding Speed of A**:
- Since A's speed is \( v + 5 \):
\[ \text{Speed of A} = 9 + 5 = 14 \text{ km/h} \]

**Final Answer**: The speed of A is 14 km/h.