A boat cover 11.2 km distance in downstream in 48 minutes. If ratio between speed of boat in still water to speed of stream is 3:1, then find in what time boat
will cover 42 km of distance in downstream and in upstream?

Options

A. A)7 hours
B. B)5 hours
C. C)9 hours
D. D)10 hours

Answer

To solve the problem step by step, we will follow the given information and derive the required values.

### Step 1: Understand the Given Information
- Distance covered downstream = 11.2 km
- Time taken downstream = 48 minutes
- Ratio of speed of boat in still water to speed of stream = 3:1

### Step 2: Convert Time from Minutes to Hours
Since speed is typically measured in km/h, we need to convert the time from minutes to hours.
- Time in hours = 48 minutes ÷ 60 = 0.8 hours

### Step 3: Calculate Downstream Speed
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
We can calculate the downstream speed:
\[ \text{Downstream Speed} = \frac{11.2 \text{ km}}{0.8 \text{ hours}} = 14 \text{ km/h} \]

### Step 4: Define Variables for Speed of Boat and Stream
Let the speed of the stream be \( k \) km/h. According to the ratio given:
- Speed of boat in still water = \( 3k \)
- Downstream speed = Speed of boat + Speed of stream = \( 3k + k = 4k \)

### Step 5: Set Up the Equation for Downstream Speed
From our calculation in Step 3:
\[ 4k = 14 \]
Now, solve for \( k \):
\[ k = \frac{14}{4} = 3.5 \text{ km/h} \]

### Step 6: Calculate Speed of Boat in Still Water
Now, calculate the speed of the boat in still water:
\[ \text{Speed of boat} = 3k = 3 \times 3.5 = 10.5 \text{ km/h} \]

### Step 7: Calculate Upstream Speed
The upstream speed can be calculated as:
\[ \text{Upstream Speed} = \text{Speed of boat} - \text{Speed of stream} = 3k - k = 2k \]
Substituting the value of \( k \):
\[ \text{Upstream Speed} = 2 \times 3.5 = 7 \text{ km/h} \]

### Step 8: Calculate Time to Cover 42 km in Downstream and Upstream
1. **Downstream Time**:
\[ \text{Time}_{\text{downstream}} = \frac{\text{Distance}}{\text{Speed}} = \frac{42 \text{ km}}{14 \text{ km/h}} = 3 \text{ hours} \]

2. **Upstream Time**:
\[ \text{Time}_{\text{upstream}} = \frac{42 \text{ km}}{7 \text{ km/h}} = 6 \text{ hours} \]

### Step 9: Total Time Calculation
Now, add both times to get the total time:
\[ \text{Total Time} = \text{Time}_{\text{downstream}} + \text{Time}_{\text{upstream}} = 3 \text{ hours} + 6 \text{ hours} = 9 \text{ hours} \]

### Final Answer
The total time taken by the boat to cover 42 km downstream and upstream is **9 hours**.

---