When a boat travels in a river (strictly in a straight line), it can go either in the direction of flow of river (i.e downstream) or in the direction opposite the flow of river (i.e. upstrem ). Thus the boat's actual speed is more than by which it can move in stationary water while travelling downstram (as river's flow speed is added to it) and less while travelling upstream (as the boat moves against the flow of river).Based on the given information answer the following questions A boat going downstream in a following river overcome a raft at a point P. 1 h later it turned back and after some time passed the raft at a distance 6 km from point P.
After reversing its direction ,how much time was taken by the boat to meet the raft again ( i.e. `2^(nd)` time) ?

Options

A. 2h
B. 1 h
C. 30 min
D. 3h

Answer

To solve the problem step by step, we will analyze the motion of the boat and the raft in the river.

### Step 1: Understand the scenario
- The boat travels downstream and meets the raft at point P.
- After 1 hour, the boat turns back upstream and meets the raft again at a distance of 6 km from point P.

### Step 2: Define variables
- Let the speed of the boat in still water be \( V \) km/h.
- Let the speed of the river current be \( U \) km/h.
- The speed of the boat downstream (with the current) is \( V + U \) km/h.
- The speed of the boat upstream (against the current) is \( V - U \) km/h.
- The speed of the raft (which is floating with the current) is \( U \) km/h.

### Step 3: Calculate the distance traveled by the boat and the raft
- In 1 hour, the distance traveled by the boat downstream is:
\[ D_{boat} = (V + U) \times 1 = V + U \text{ km} \]
- In the same time, the distance traveled by the raft is:
\[ D_{raft} = U \times 1 = U \text{ km} \]

### Step 4: Determine the distance between the boat and the raft after 1 hour
- After 1 hour, the distance between the boat and the raft is:
\[ \text{Distance} = D_{boat} - D_{raft} = (V + U) - U = V \text{ km} \]

### Step 5: Analyze the return journey of the boat
- After 1 hour, the boat turns back and travels upstream.
- Let \( t \) be the time taken by the boat to meet the raft again after turning back.

### Step 6: Set up the equations for the meeting point
- In time \( t \), the distance traveled by the boat upstream is:
\[ D_{boat\_upstream} = (V - U) \times t \]
- The distance traveled by the raft in the same time is:
\[ D_{raft} = U \times t \]

### Step 7: Set up the equation for the total distance
- The total distance covered by both the boat and the raft when they meet again is equal to the initial distance \( V \):
\[ (V - U) \times t + U \times t = V \]
- Simplifying this gives:
\[ Vt - Ut + Ut = V \]
\[ Vt = V \]

### Step 8: Solve for \( t \)
- Dividing both sides by \( V \) (assuming \( V \neq 0 \)):
\[ t = 1 \text{ hour} \]

### Final Answer
The time taken by the boat to meet the raft again after reversing its direction is **1 hour**.

---