The downstream speed of a boat is 42 km/hr and the speed of current is 3 km/hr. What is the total time (in hours) taken by the boat to cover 72 km upstream and 84 km downstream?

Options

A. 3
B. 4
C. 5
D. 6

Answer

To solve the problem of calculating the total time taken by the boat to cover 72 km upstream and 84 km downstream, we will follow these steps:

### Step 1: Determine the speeds of the boat upstream and downstream.
- The downstream speed of the boat is given as 42 km/hr.
- The speed of the current is 3 km/hr.
- To find the upstream speed, we subtract the speed of the current from the downstream speed.

**Calculation:**
\[ \text{Upstream Speed} = \text{Downstream Speed} - \text{Speed of Current} \]
\[ \text{Upstream Speed} = 42 \text{ km/hr} - 3 \text{ km/hr} = 39 \text{ km/hr} \]

### Step 2: Calculate the time taken to travel upstream.
- The distance to be covered upstream is 72 km.
- We use the formula for time, which is distance divided by speed.

**Calculation:**
\[ \text{Time Upstream} = \frac{\text{Distance Upstream}}{\text{Upstream Speed}} \]
\[ \text{Time Upstream} = \frac{72 \text{ km}}{39 \text{ km/hr}} \]
\[ \text{Time Upstream} = \frac{72}{39} \approx 1.846 \text{ hours} \]

### Step 3: Calculate the time taken to travel downstream.
- The distance to be covered downstream is 84 km.
- We use the same formula for time.

**Calculation:**
\[ \text{Time Downstream} = \frac{\text{Distance Downstream}}{\text{Downstream Speed}} \]
\[ \text{Time Downstream} = \frac{84 \text{ km}}{42 \text{ km/hr}} \]
\[ \text{Time Downstream} = 2 \text{ hours} \]

### Step 4: Calculate the total time taken.
- The total time is the sum of the time taken upstream and downstream.

**Calculation:**
\[ \text{Total Time} = \text{Time Upstream} + \text{Time Downstream} \]
\[ \text{Total Time} = 1.846 \text{ hours} + 2 \text{ hours} \]
\[ \text{Total Time} \approx 3.846 \text{ hours} \]

### Final Answer:
The total time taken by the boat to cover 72 km upstream and 84 km downstream is approximately **3.846 hours**.

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