A boat takes 4 hrs to cover 'D' km in upstream and takes 3 hours to cover 'D-2 km in downstream. If speed of stream is 2 kmph, then find distance covered by boat in upstream in 3 hrs.

Options

A. A)44 km
B. B)48 km
C. C)42 km
D. D)56 km

Answer

To solve the problem step by step, we need to find the distance covered by the boat in upstream in 3 hours, given the conditions of the problem.

### Step 1: Define Variables
Let:
- \( b \) = speed of the boat in still water (in km/h)
- Speed of the stream = 2 km/h

### Step 2: Calculate Upstream Distance
The distance covered by the boat in upstream is \( D \) km, and it takes 4 hours to cover this distance. The speed of the boat in upstream is given by:
\[ \text{Speed}_{\text{upstream}} = b - 2 \]
Using the formula for distance, we have:
\[ D = \text{Time} \times \text{Speed} = 4(b - 2) \]
Thus, we can express \( D \) as:
\[ D = 4b - 8 \quad \text{(Equation 1)} \]

### Step 3: Calculate Downstream Distance
The distance covered in downstream is \( D - 2 \) km, and it takes 3 hours to cover this distance. The speed of the boat in downstream is:
\[ \text{Speed}_{\text{downstream}} = b + 2 \]
Using the distance formula again, we have:
\[ D - 2 = \text{Time} \times \text{Speed} = 3(b + 2) \]
Thus, we can express \( D - 2 \) as:
\[ D - 2 = 3b + 6 \quad \text{(Equation 2)} \]

### Step 4: Substitute Equation 1 into Equation 2
From Equation 1, we know \( D = 4b - 8 \). Substitute this into Equation 2:
\[ (4b - 8) - 2 = 3b + 6 \]
This simplifies to:
\[ 4b - 10 = 3b + 6 \]

### Step 5: Solve for \( b \)
Now, rearranging the equation gives:
\[ 4b - 3b = 10 + 6 \]
\[ b = 16 \quad \text{(Speed of the boat in still water)} \]

### Step 6: Calculate Upstream Speed
Now that we have the speed of the boat, we can find the upstream speed:
\[ \text{Speed}_{\text{upstream}} = b - 2 = 16 - 2 = 14 \text{ km/h} \]

### Step 7: Calculate Distance Covered in 3 Hours Upstream
Finally, to find the distance covered in upstream in 3 hours:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 14 \times 3 = 42 \text{ km} \]

### Final Answer
The distance covered by the boat in upstream in 3 hours is **42 km**.

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