The speed of a boat in still water is 20 km/h and the speed of the stream is 5 km/h. Find the total taken to travel a distance of 30 km upstream and 50 km downstream.
(A) Find the speed of the boar downstream.
(B) Recall the formula: `" Time "=(" distance ")/(" speed ")`
(C ) Find the speed of the boat upstream.
(D) Required time `=(30)/(15)+(50)/(25)=2+2=4h`

Options

A. ABCD
B. DABC
C. CADBE
D. ACBD

Answer

To solve the problem step by step, we will follow the instructions given in the question and the video transcript.

### Step 1: Find the speed of the boat downstream
The speed of the boat in still water is given as 20 km/h, and the speed of the stream is 5 km/h.

**Downstream speed formula:**
\[ \text{Speed downstream} = \text{Speed of boat} + \text{Speed of stream} \]
\[ \text{Speed downstream} = 20 \text{ km/h} + 5 \text{ km/h} = 25 \text{ km/h} \]

### Step 2: Recall the formula for time
The formula to calculate time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 3: Find the speed of the boat upstream
**Upstream speed formula:**
\[ \text{Speed upstream} = \text{Speed of boat} - \text{Speed of stream} \]
\[ \text{Speed upstream} = 20 \text{ km/h} - 5 \text{ km/h} = 15 \text{ km/h} \]

### Step 4: Calculate the time taken to travel upstream
The distance to travel upstream is 30 km.

Using the time formula:
\[ \text{Time upstream} = \frac{\text{Distance upstream}}{\text{Speed upstream}} \]
\[ \text{Time upstream} = \frac{30 \text{ km}}{15 \text{ km/h}} = 2 \text{ hours} \]

### Step 5: Calculate the time taken to travel downstream
The distance to travel downstream is 50 km.

Using the time formula:
\[ \text{Time downstream} = \frac{\text{Distance downstream}}{\text{Speed downstream}} \]
\[ \text{Time downstream} = \frac{50 \text{ km}}{25 \text{ km/h}} = 2 \text{ hours} \]

### Step 6: Calculate the total time taken
Now, we add the time taken for both upstream and downstream travel:
\[ \text{Total time} = \text{Time upstream} + \text{Time downstream} \]
\[ \text{Total time} = 2 \text{ hours} + 2 \text{ hours} = 4 \text{ hours} \]

### Final Answer
The total time taken to travel 30 km upstream and 50 km downstream is **4 hours**.

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