A man can row 8 km in 1 h in still water . If the speed of the water current is 2 kmpj and it takes 3 h for him to go from a point P to Q and return to P . then find the distance PQ

Answer

To solve the problem, we need to find the distance between points P and Q (denoted as PQ). We know the following:

1. The man's rowing speed in still water = 8 km/h
2. The speed of the water current = 2 km/h
3. The total time taken for the round trip from P to Q and back to P = 3 hours

### Step 1: Calculate the effective speeds
When rowing downstream (from P to Q), the effective speed of the man will be the sum of his rowing speed and the current speed:

- Downstream speed = Speed in still water + Speed of current
- Downstream speed = 8 km/h + 2 km/h = 10 km/h

When rowing upstream (from Q to P), the effective speed will be the difference between his rowing speed and the current speed:

- Upstream speed = Speed in still water - Speed of current
- Upstream speed = 8 km/h - 2 km/h = 6 km/h

### Step 2: Let the distance PQ be 'd' km
We can express the time taken to travel downstream and upstream in terms of 'd':

- Time taken to go from P to Q (downstream) = Distance / Speed = d / 10 hours
- Time taken to return from Q to P (upstream) = Distance / Speed = d / 6 hours

### Step 3: Set up the equation for total time
The total time for the round trip is given as 3 hours. Therefore, we can set up the equation:

\[ \frac{d}{10} + \frac{d}{6} = 3 \]

### Step 4: Solve the equation
To solve this equation, we need to find a common denominator. The least common multiple of 10 and 6 is 30. We can rewrite the equation:

\[ \frac{3d}{30} + \frac{5d}{30} = 3 \]

Combining the fractions gives:

\[ \frac{8d}{30} = 3 \]

Now, multiply both sides by 30 to eliminate the fraction:

\[ 8d = 90 \]

Now, divide both sides by 8:

\[ d = \frac{90}{8} = 11.25 \text{ km} \]

### Conclusion
The distance PQ is 11.25 km.