The speed of a boat in still water is 8 kmph and the speed of stream is 6 kmph . The boat covers a round - trip journey in 12 h. Find the time taken by it to complete the upstream journey ?

Options

A. `10(1)/(2) h`
B. `9 (3)/(4) h`
C. `10 (1)/(4)` h
D. `9 (1)/(4) h `

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Speeds
- Speed of the boat in still water = 8 km/h
- Speed of the stream = 6 km/h

### Step 2: Calculate Upstream and Downstream Speeds
- **Upstream speed** (against the current) = Speed of boat - Speed of stream
\[ \text{Upstream speed} = 8 \text{ km/h} - 6 \text{ km/h} = 2 \text{ km/h} \]

- **Downstream speed** (with the current) = Speed of boat + Speed of stream
\[ \text{Downstream speed} = 8 \text{ km/h} + 6 \text{ km/h} = 14 \text{ km/h} \]

### Step 3: Let the Distance be 'd'
Assume the distance for one way (upstream or downstream) is 'd' km.

### Step 4: Write the Time Equations
- **Time taken to go upstream** = Distance / Upstream speed
\[ \text{Time upstream} = \frac{d}{2} \]

- **Time taken to go downstream** = Distance / Downstream speed
\[ \text{Time downstream} = \frac{d}{14} \]

### Step 5: Total Time for Round Trip
The total time for the round trip is given as 12 hours.
\[ \text{Total time} = \text{Time upstream} + \text{Time downstream} = 12 \]
\[ \frac{d}{2} + \frac{d}{14} = 12 \]

### Step 6: Solve for 'd'
To solve the equation, we need a common denominator. The least common multiple (LCM) of 2 and 14 is 14.
\[ \frac{7d}{14} + \frac{d}{14} = 12 \]
\[ \frac{8d}{14} = 12 \]
\[ 8d = 12 \times 14 \]
\[ 8d = 168 \]
\[ d = \frac{168}{8} = 21 \text{ km} \]

### Step 7: Calculate Time Taken for Upstream Journey
Now, we can find the time taken to complete the upstream journey.
\[ \text{Time upstream} = \frac{d}{2} = \frac{21}{2} = 10.5 \text{ hours} \]

### Final Answer
The time taken by the boat to complete the upstream journey is **10.5 hours**.

---