The difference between downstream speed and upstream speed of boat 6km/hr and boat travels 72 km from P to Q (downstream) in 4 hours. Find the speed of boat in still water.

Options

A. 15km/hr
B. 18km/hr
C. 20km/hr
D. 16km/hr

Answer

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

### Step 1: Understand the given information
- The difference between the downstream speed and upstream speed of the boat is 6 km/hr.
- The boat travels 72 km downstream from P to Q in 4 hours.

### Step 2: Calculate the downstream speed
Since the boat travels 72 km downstream in 4 hours, we can calculate the downstream speed using the formula:
\[ \text{Downstream Speed} = \frac{\text{Distance}}{\text{Time}} \]
\[ \text{Downstream Speed} = \frac{72 \text{ km}}{4 \text{ hr}} = 18 \text{ km/hr} \]

### Step 3: Set up the equations
Let the speed of the boat in still water be \( x \) km/hr, and let the speed of the current be \( y \) km/hr. We know:
1. Downstream speed = \( x + y \)
2. Upstream speed = \( x - y \)
3. The difference between downstream and upstream speeds = 6 km/hr

From the above information, we can write:
\[ (x + y) - (x - y) = 6 \]
This simplifies to:
\[ 2y = 6 \]
Thus, we find:
\[ y = 3 \text{ km/hr} \]

### Step 4: Substitute the value of \( y \) to find \( x \)
Now, we can use the downstream speed to find \( x \):
\[ x + y = 18 \text{ km/hr} \]
Substituting \( y = 3 \):
\[ x + 3 = 18 \]
\[ x = 18 - 3 \]
\[ x = 15 \text{ km/hr} \]

### Step 5: Conclusion
The speed of the boat in still water is \( 15 \) km/hr.

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