A boat sails 15 km of a river towards upstream in 5 hours how long will it take to cover the same distance downstream if the speed of current is one fourth the speed of the boat in still water:

Options

A. 1.8 h
B. 3 h
C. 4 h
D. 5 h

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the speed of the current be \( x \) km/h. Therefore, the speed of the boat in still water will be \( 4x \) km/h.

### Step 2: Calculate the Upstream Speed
When the boat is going upstream, it is moving against the current. The effective speed of the boat upstream is given by:
\[ \text{Speed upstream} = \text{Speed of boat} - \text{Speed of current} = 4x - x = 3x \text{ km/h} \]

### Step 3: Use Given Information to Find \( x \)
We know that the boat sails 15 km upstream in 5 hours. We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Rearranging this gives us:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{15 \text{ km}}{5 \text{ hours}} = 3 \text{ km/h} \]
Thus, we have:
\[ 3x = 3 \implies x = 1 \text{ km/h} \]

### Step 4: Calculate the Downstream Speed
Now, we can find the speed of the boat downstream. The effective speed downstream is:
\[ \text{Speed downstream} = \text{Speed of boat} + \text{Speed of current} = 4x + x = 5x \]
Substituting \( x = 1 \):
\[ \text{Speed downstream} = 5 \times 1 = 5 \text{ km/h} \]

### Step 5: Calculate the Time Taken to Travel Downstream
Now, we need to find the time taken to cover the same distance of 15 km downstream. Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{15 \text{ km}}{5 \text{ km/h}} = 3 \text{ hours} \]

### Final Answer
The time taken to cover the same distance downstream is **3 hours**.

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