A boat covered 20km downstream and 28 km upstream. The speed of boat in still water is 7 km/hr and speed of stream is 3 km/hr. Find the time taken to complete the whole journey.

Options

A. A)9 hours
B. B)8 hours
C. C)6 hours
D. D)10 hours

Answer

To solve the problem step by step, we need to determine the time taken for the boat to travel downstream and upstream, and then sum these times to find the total journey time.

### Step 1: Determine the speeds
- **Speed of the boat in still water (B)** = 7 km/hr
- **Speed of the stream (S)** = 3 km/hr

### Step 2: Calculate downstream speed
- **Downstream speed (D)** = Speed of boat + Speed of stream
\[ D = B + S = 7 \text{ km/hr} + 3 \text{ km/hr} = 10 \text{ km/hr} \]

### Step 3: Calculate upstream speed
- **Upstream speed (U)** = Speed of boat - Speed of stream
\[ U = B - S = 7 \text{ km/hr} - 3 \text{ km/hr} = 4 \text{ km/hr} \]

### Step 4: Calculate time taken to travel downstream
- **Distance downstream** = 20 km
- **Time taken downstream (T_d)** = Distance / Downstream speed
\[ T_d = \frac{20 \text{ km}}{10 \text{ km/hr}} = 2 \text{ hours} \]

### Step 5: Calculate time taken to travel upstream
- **Distance upstream** = 28 km
- **Time taken upstream (T_u)** = Distance / Upstream speed
\[ T_u = \frac{28 \text{ km}}{4 \text{ km/hr}} = 7 \text{ hours} \]

### Step 6: Calculate total time taken for the journey
- **Total time (T_total)** = Time downstream + Time upstream
\[ T_total = T_d + T_u = 2 \text{ hours} + 7 \text{ hours} = 9 \text{ hours} \]

### Final Answer
The total time taken to complete the whole journey is **9 hours**.

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