A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is

Given the same problem:

- Speed of motorboat in still water = \( 15 \) km/h
- Downstream distance = Upstream distance = 30 km
- Total time = 4 hours 30 minutes = \( 4.5 \) hours

Let the speed of the stream be \( x \) km/h.

### Equations for downstream and upstream:
- **Downstream speed** = \( 15 + x \) km/h
- **Upstream speed** = \( 15 - x \) km/h

The time taken for downstream and upstream travel is:
\[
\frac{30}{15 + x} + \frac{30}{15 - x} = 4.5
\]

I'll solve this equation again to determine the speed of the stream, as you asked for it directly.# Re-solving the equation based on the same problem setup
speed_of_stream = solve(total_time_eq, x)
speed_of_streamThe speed of the stream is \( 5 \) km/h.

Would you like more clarification on the process, or any additional details?

Here are five related questions:
1. How would the time change if the stream speed were reduced to 3 km/h?
2. What happens if the boat's speed in still water increases to 20 km/h?
3. How can you calculate the time for just one leg of the journey (downstream or upstream)?
4. What other factors could affect a boat’s speed in a real-life scenario on a river?
5. How would the problem be different if the boat traveled on a circular path rather than a straight river?

**Tip:** Always verify that the solution satisfies the physical conditions of the problem, such as keeping speed positive.

Learn how to calculate the speed of a stream using a motorboat's speed in still water and total travel time. This problem involves solving linear equations and understanding the relationship between speed, distance, and time. Suitable for students in Grades 9-12.

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