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 the water current respectively?

Options

A. `2:1`
B. `3:2`
C. `8:3`
D. None of these

Answer

To solve the problem, we need to find the ratio between the speed of the boat and the speed of the water current based on the time taken to travel the same distance upstream and downstream.

### Step-by-Step Solution:

1. **Convert Time to Hours**:
- The time taken to travel upstream is given as 8 hours and 48 minutes.
- Convert 48 minutes into hours:
\[ 48 \text{ minutes} = \frac{48}{60} = \frac{4}{5} \text{ hours} \]
- Therefore, the total time upstream is:
\[ 8 \text{ hours} + \frac{4}{5} \text{ hours} = 8 + 0.8 = 8.8 \text{ hours} = \frac{44}{5} \text{ hours} \]

2. **Time Taken Downstream**:
- The time taken to travel downstream is given as 4 hours.

3. **Set Up the Ratio of Times**:
- The ratio of the time taken upstream to the time taken downstream is:
\[ \text{Time ratio} = \frac{\text{Time upstream}}{\text{Time downstream}} = \frac{\frac{44}{5}}{4} = \frac{44}{5} \times \frac{1}{4} = \frac{44}{20} = \frac{11}{5} \]

4. **Use the Time Ratio to Find Speed Ratio**:
- Since the distance is the same, the speed ratio is the inverse of the time ratio:
\[ \text{Speed ratio} = \frac{\text{Downstream speed}}{\text{Upstream speed}} = \frac{5}{11} \]

5. **Let Speeds be Represented in Terms of x**:
- Let the speed of the boat be \( 11x \) and the speed of the current be \( 5x \).

6. **Apply the Speed Formulas**:
- The speed of the boat (B) is given by:
\[ B = \frac{\text{Downstream speed} + \text{Upstream speed}}{2} = \frac{11x + 5x}{2} = \frac{16x}{2} = 8x \]
- The speed of the current (S) is given by:
\[ S = \frac{\text{Downstream speed} - \text{Upstream speed}}{2} = \frac{11x - 5x}{2} = \frac{6x}{2} = 3x \]

7. **Find the Ratio of Boat Speed to Current Speed**:
- The ratio of the speed of the boat to the speed of the current is:
\[ \text{Ratio} = \frac{B}{S} = \frac{8x}{3x} = \frac{8}{3} \]

### Final Answer:
The ratio between the speed of the boat and the speed of the water current is:
\[ \text{Ratio} = 8 : 3 \]