A boat goes 7 km upstream in 42 minutes. If the speed of the stream is 3 km/h, what is the speed of the boat in still water (in km/h)?

Introduction / Context:
In this boats and streams question you must derive the boat speed in still water from an upstream journey and a known stream speed. This requires converting time properly, computing the effective upstream speed, and then adding the current speed to recover the still water speed.

Given Data / Assumptions:
- Upstream distance = 7 km. - Time taken upstream = 42 minutes. - Speed of the stream = 3 km/h. - Let b be the speed of the boat in still water (km/h). - Upstream speed = b - 3 km/h.

Concept / Approach:
First, convert the time from minutes to hours to keep units consistent. Then use speed = distance / time to find the upstream speed. Since upstream speed equals b minus the stream speed, we can solve for b by adding the current speed to the upstream speed. This is a direct application of the definition of upstream speed.

Step-by-Step Solution:
Step 1: Convert 42 minutes to hours: 42 / 60 hours = 0.7 hour. Step 2: Upstream speed = distance / time = 7 / 0.7 km/h. Step 3: 7 / 0.7 = 10 km/h (because 0.7 * 10 = 7). Step 4: Let b be the speed of the boat in still water. Step 5: Upstream speed = b - stream speed, so b - 3 = 10. Step 6: Solve for b: b = 10 + 3 = 13 km/h.

Verification / Alternative check:
If the boat speed in still water is 13 km/h and the stream is 3 km/h, the upstream speed is 13 - 3 = 10 km/h. For a 7 km journey, time taken upstream = 7 / 10 hours = 0.7 hour = 42 minutes, exactly matching the data. Therefore, 13 km/h is consistent with the given journey details.

Why Other Options Are Wrong:
- 14 km/h would give upstream speed 11 km/h and an upstream time of 7 / 11 hours, not equal to 42 minutes. - 12 km/h would give upstream speed 9 km/h and a time that is longer than 42 minutes. - 11 km/h and 10 km/h correspond to even lower still water speeds and do not satisfy the 7 km in 42 minutes condition when combined with 3 km/h current.

Common Pitfalls:
Learners sometimes forget to convert minutes into hours or miscalculate 7 / 0.7. Others mistakenly subtract the upstream speed from the current instead of adding the current to the upstream speed to get b. Carefully tracking units and using the formula upstream speed = b - c helps avoid such mistakes.

Final Answer:
The speed of the boat in still water is 13 km/h.