A boat covers a certain distance downstream in 8 hours and comes back upstream in 10 hours. If the speed of the current be 1 km/hr, the distance (in km) of the one way journey is

Options

A. 60
B. 70
C. 80
D. 90

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define Variables
Let the speed of the boat in still water be \( x \) km/hr. The speed of the current is given as 1 km/hr.

### Step 2: Determine Speeds
- **Downstream Speed**: When the boat is going downstream, the speed is the sum of the speed of the boat and the speed of the current:
\[ \text{Downstream Speed} = x + 1 \text{ km/hr} \]
- **Upstream Speed**: When the boat is going upstream, the speed is the difference between the speed of the boat and the speed of the current:
\[ \text{Upstream Speed} = x - 1 \text{ km/hr} \]

### Step 3: Set Up Distance Equations
The distance covered downstream and upstream is the same. We can express the distance using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

- **Distance Downstream**:
\[ \text{Distance} = (x + 1) \times 8 \]
- **Distance Upstream**:
\[ \text{Distance} = (x - 1) \times 10 \]

### Step 4: Equate the Distances
Since the distance downstream is equal to the distance upstream, we can set the two equations equal to each other:
\[ (x + 1) \times 8 = (x - 1) \times 10 \]

### Step 5: Expand and Simplify the Equation
Expanding both sides:
\[ 8x + 8 = 10x - 10 \]

Now, rearranging the equation:
\[ 8x + 8 + 10 = 10x \]
\[ 8x + 18 = 10x \]

Subtract \( 8x \) from both sides:
\[ 18 = 10x - 8x \]
\[ 18 = 2x \]

### Step 6: Solve for \( x \)
Dividing both sides by 2:
\[ x = 9 \text{ km/hr} \]

### Step 7: Calculate the Distance
Now that we have the speed of the boat in still water, we can find the distance using either the downstream or upstream equation. Using the downstream equation:
\[ \text{Distance} = (x + 1) \times 8 \]
Substituting \( x = 9 \):
\[ \text{Distance} = (9 + 1) \times 8 = 10 \times 8 = 80 \text{ km} \]

### Final Answer
The distance of the one-way journey is **80 km**.

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