A boat covers 36 km downstream in 6 hours, which is 3 hours less than the time it takes to cover the same distance upstream. What is the speed of the stream (in km/h)?

Introduction / Context:
Here you are asked to infer the speed of the stream using information about how long the same distance takes downstream and upstream. This is a standard boats and streams problem where times and distances are given instead of speeds directly, and you must work backwards to the current speed.

Given Data / Assumptions:
- Distance downstream and upstream = 36 km. - Downstream time = 6 hours. - Upstream time is 3 hours more, so upstream time = 9 hours. - Let b be the speed in still water, c be the speed of the stream. - Downstream speed = b + c, upstream speed = b - c.

Concept / Approach:
First find effective downstream and upstream speeds from distance / time. Then use the two equations b + c = downstream speed and b - c = upstream speed. Solving these simultaneous equations yields both the boat speed in still water and the stream speed. Our interest here is the stream speed c.

Step-by-Step Solution:
Step 1: Downstream speed = 36 / 6 = 6 km/h. Step 2: Upstream time = 6 + 3 = 9 hours. Step 3: Upstream speed = 36 / 9 = 4 km/h. Step 4: So b + c = 6 and b - c = 4. Step 5: Add the equations: (b + c) + (b - c) = 6 + 4, giving 2b = 10. Step 6: Hence b = 10 / 2 = 5 km/h. Step 7: Substitute into b + c = 6: 5 + c = 6, so c = 1 km/h.

Verification / Alternative check:
With b = 5 km/h and c = 1 km/h, downstream speed = 6 km/h and upstream speed = 4 km/h. Time downstream = 36 / 6 = 6 hours. Time upstream = 36 / 4 = 9 hours, which is exactly 3 hours more than the downstream time. So the stream speed of 1 km/h is consistent with all given information.

Why Other Options Are Wrong:
- 1.5, 0.75, and 0.5 km/h would all produce upstream and downstream speeds that do not result in times of 6 and 9 hours for 36 km. - 2 km/h would give upstream speed 3 km/h, leading to 12 hours upstream, not 9 hours.

Common Pitfalls:
Some learners mistakenly subtract the times or distances directly to get the stream speed or confuse upstream and downstream speeds. Others incorrectly average times instead of working with speeds. Always convert time and distance into speeds first, then use the b + c and b - c system of equations.

Final Answer:
The speed of the stream is 1 km/h.