A boat covers 20 km in an hour with downstream and covers the same distance in 2 h with upstream. Then, find the speed of boat in still water and speed of stream.

Answer

To solve the problem, we need to find the speed of the boat in still water (b) and the speed of the stream (s). We will use the information given about the downstream and upstream travel times and distances.

### Step-by-Step Solution:

1. **Identify the given data:**
- Distance covered downstream (d) = 20 km
- Time taken downstream (t_d) = 1 hour
- Time taken upstream (t_u) = 2 hours

2. **Calculate the speed downstream:**
- Speed downstream (b + s) = Distance / Time
- Speed downstream = 20 km / 1 hour = 20 km/h

3. **Calculate the speed upstream:**
- Speed upstream (b - s) = Distance / Time
- Speed upstream = 20 km / 2 hours = 10 km/h

4. **Set up the equations:**
- From the downstream speed, we have:
\[ b + s = 20 \quad \text{(Equation 1)} \]
- From the upstream speed, we have:
\[ b - s = 10 \quad \text{(Equation 2)} \]

5. **Solve the equations simultaneously:**
- Add Equation 1 and Equation 2:
\[ (b + s) + (b - s) = 20 + 10 \]
\[ 2b = 30 \]
\[ b = 15 \text{ km/h} \quad \text{(Speed of the boat in still water)} \]

6. **Substitute b back to find s:**
- Substitute b = 15 into Equation 1:
\[ 15 + s = 20 \]
\[ s = 20 - 15 = 5 \text{ km/h} \quad \text{(Speed of the stream)} \]

### Final Answers:
- Speed of the boat in still water (b) = 15 km/h
- Speed of the stream (s) = 5 km/h

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