A boat which sails at 10 km/h in still water starts chasing from 10 km behind another one which sails at 4 km/h in the upstream directions after how lonf will it catchup if the stream is flowing at 2 km/h:

Options

A. 4 h
B. 2.5 h
C. 2h
D. 3.5 h

Answer

To solve the problem of how long it will take for the faster boat to catch up with the slower boat, we can follow these steps:

### Step 1: Determine the effective speed of the first boat (Boat 1)
The speed of Boat 1 in still water is 10 km/h. Since it is moving upstream against the current of the stream, we need to subtract the speed of the stream (2 km/h) from the speed of Boat 1.

**Calculation:**
\[ \text{Speed of Boat 1} = 10 \text{ km/h} - 2 \text{ km/h} = 8 \text{ km/h} \]

### Step 2: Determine the speed of the second boat (Boat 2)
The speed of Boat 2 is given as 4 km/h, and since it is also moving upstream, we do not need to adjust this speed.

**Speed of Boat 2:**
\[ \text{Speed of Boat 2} = 4 \text{ km/h} \]

### Step 3: Calculate the relative speed between the two boats
Since both boats are moving in the same direction, the relative speed is the difference between the speeds of Boat 1 and Boat 2.

**Calculation:**
\[ \text{Relative Speed} = \text{Speed of Boat 1} - \text{Speed of Boat 2} \]
\[ \text{Relative Speed} = 8 \text{ km/h} - 4 \text{ km/h} = 4 \text{ km/h} \]

### Step 4: Determine the distance between the two boats
The initial distance between the two boats is given as 10 km.

### Step 5: Calculate the time taken to catch up
Using the formula for time, which is distance divided by speed, we can find the time it takes for Boat 1 to catch up with Boat 2.

**Calculation:**
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
\[ \text{Time} = \frac{10 \text{ km}}{4 \text{ km/h}} = 2.5 \text{ hours} \]

### Final Answer:
The first boat will catch up with the second boat in **2.5 hours**.

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