A boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . What is the ratio between the speed of the boat and speed of water current respectively ?

Options

A. `2 :1`
B. `3:2`
C. `8:3`
D. Cannot be determined

Explanation

To solve the problem, we need to find the ratio between the speed of the boat (B) and the speed of the water current (W). Let's break it down step by step.

### Step 1: Convert Time into Hours
The boat takes 8 hours and 48 minutes to travel upstream. We need to convert this time into hours.
- 48 minutes = 48/60 hours = 0.8 hours
- Therefore, total time upstream = 8 + 0.8 = 8.8 hours.

### Step 2: Define Variables
Let:
- \( B \) = speed of the boat in still water (in km/h)
- \( W \) = speed of the water current (in km/h)
- Upstream speed \( S_u = B - W \)
- Downstream speed \( S_d = B + W \)

### Step 3: Write Distance Equations
The distance covered upstream and downstream is the same. We can express this as:
- Distance upstream = \( S_u \times \text{Time upstream} = (B - W) \times 8.8 \)
- Distance downstream = \( S_d \times \text{Time downstream} = (B + W) \times 4 \)

Since both distances are equal, we have:
\[ (B - W) \times 8.8 = (B + W) \times 4 \]

### Step 4: Expand and Rearrange the Equation
Expanding the equation gives us:
\[ 8.8B - 8.8W = 4B + 4W \]
Rearranging this, we get:
\[ 8.8B - 4B = 4W + 8.8W \]
\[ 4.8B = 12.8W \]

### Step 5: Solve for the Ratio
Now, we can find the ratio of \( B \) to \( W \):
\[ \frac{B}{W} = \frac{12.8}{4.8} \]
Simplifying this fraction:
\[ \frac{B}{W} = \frac{12.8 \div 4.8}{4.8 \div 4.8} = \frac{2.6667}{1} \approx \frac{8}{3} \]

### Final Step: Write the Ratio
Thus, the ratio of the speed of the boat to the speed of the water current is:
\[ \text{Ratio} = 8:3 \]