The speed of a boat downstream is 15km/hr and the speed of current is 3 km/hr. Find the total time taken by the boat to cover 15 km upstream and 15 km downstream.

Options

A. 2 hours 40 minutes
B. 2 hours 42 minutes
C. 3 hours 10 minutes
D. 2 hours 30 minutes

Answer

To solve the problem, we need to find the total time taken by the boat to cover 15 km upstream and 15 km downstream. We will follow these steps:

### Step 1: Determine the speed of the boat in still water
The speed of the boat downstream is given as 15 km/hr, and the speed of the current is 3 km/hr. The speed of the boat in still water (B) can be calculated using the formula:

\[ B + C = D \]

Where:
- \( B \) = speed of the boat in still water
- \( C \) = speed of the current
- \( D \) = speed of the boat downstream

Substituting the known values:

\[ B + 3 = 15 \]

### Step 2: Solve for the speed of the boat in still water
Rearranging the equation gives us:

\[ B = 15 - 3 \]
\[ B = 12 \text{ km/hr} \]

### Step 3: Calculate the speed of the boat upstream
The speed of the boat upstream (U) can be calculated using the formula:

\[ U = B - C \]

Substituting the known values:

\[ U = 12 - 3 \]
\[ U = 9 \text{ km/hr} \]

### Step 4: Calculate the time taken to travel downstream
The time taken to travel a distance (D) can be calculated using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

For downstream, the distance is 15 km and the speed is 15 km/hr:

\[ \text{Time}_{\text{downstream}} = \frac{15}{15} = 1 \text{ hour} \]

### Step 5: Calculate the time taken to travel upstream
For upstream, the distance is also 15 km, but the speed is 9 km/hr:

\[ \text{Time}_{\text{upstream}} = \frac{15}{9} = \frac{5}{3} \text{ hours} \]

### Step 6: Calculate the total time taken
Now, we can find the total time taken by adding the time taken upstream and downstream:

\[ \text{Total Time} = \text{Time}_{\text{downstream}} + \text{Time}_{\text{upstream}} \]

Substituting the values:

\[ \text{Total Time} = 1 + \frac{5}{3} \]

To add these, convert 1 hour to a fraction:

\[ 1 = \frac{3}{3} \]

Thus,

\[ \text{Total Time} = \frac{3}{3} + \frac{5}{3} = \frac{8}{3} \text{ hours} \]

### Final Answer
The total time taken by the boat to cover 15 km upstream and 15 km downstream is \( \frac{8}{3} \) hours or approximately 2 hours and 40 minutes.

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