Two boats are traveling towards each other in a stream.
They both can travel at 30 kmph in still water. If they are
300 km apart how long will it take them to cross each other
if the speed of the stream is 5 kmph?

Options

A. 4 hours
B. 5 hours
C. 6 hours
D. 4.5 hours

Explanation

To solve the problem, we need to determine how long it will take for the two boats to cross each other while traveling towards each other in a stream. Here’s a step-by-step solution:

### Step 1: Determine the effective speeds of the boats
- The speed of each boat in still water = 30 km/h
- Speed of the stream = 5 km/h

For the boat moving downstream (towards each other):
- Effective speed of the first boat (downstream) = Speed in still water + Speed of the stream
\[ \text{Effective speed of Boat 1} = 30 \text{ km/h} + 5 \text{ km/h} = 35 \text{ km/h} \]

For the boat moving upstream (towards the other boat):
- Effective speed of the second boat (upstream) = Speed in still water - Speed of the stream
\[ \text{Effective speed of Boat 2} = 30 \text{ km/h} - 5 \text{ km/h} = 25 \text{ km/h} \]

### Step 2: Calculate the combined speed of both boats
- Combined speed when both boats are moving towards each other:
\[ \text{Combined speed} = \text{Effective speed of Boat 1} + \text{Effective speed of Boat 2} \]
\[ \text{Combined speed} = 35 \text{ km/h} + 25 \text{ km/h} = 60 \text{ km/h} \]

### Step 3: Determine the time taken to cross each other
- Distance between the two boats = 300 km
- Time taken to cross each other can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
\[ \text{Time} = \frac{300 \text{ km}}{60 \text{ km/h}} = 5 \text{ hours} \]

### Final Answer
The time taken for the two boats to cross each other is **5 hours**.

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