A boat can row 35 km .upstream in 7 hours and the same distance downstream in 5 hours .What is the speed (in km/hr)of the boat in still water ?

Options

A. 5
B. 7
C. 9
D. 6

Answer

To find the speed of the boat in still water, we can follow these steps:

### Step 1: Determine the speeds upstream and downstream.
- The boat rows 35 km upstream in 7 hours.
- Speed upstream = Distance / Time = 35 km / 7 hours = 5 km/hr.

- The boat rows the same distance downstream in 5 hours.
- Speed downstream = Distance / Time = 35 km / 5 hours = 7 km/hr.

### Step 2: Set up equations for the speeds.
Let:
- Speed of the boat in still water = x km/hr.
- Speed of the stream = y km/hr.

From the information given:
1. Upstream speed: \( x - y = 5 \) (Equation 1)
2. Downstream speed: \( x + y = 7 \) (Equation 2)

### Step 3: Solve the equations.
To find the values of x and y, we can add the two equations:
- Adding Equation 1 and Equation 2:
\[ (x - y) + (x + y) = 5 + 7 \]
\[ 2x = 12 \]
\[ x = 6 \]

### Step 4: Find the speed of the stream.
Now, we can substitute the value of x back into either equation to find y. Let's use Equation 1:
\[ 6 - y = 5 \]
\[ y = 6 - 5 = 1 \]

### Conclusion:
The speed of the boat in still water is **6 km/hr**.

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