The speeds of a boat along the current and against the current are 14 km/h and 7 km/h respectively. What is the speed of the boat in still water (in km/h)?

Introduction / Context:
This question directly uses the basic formulas for boats and streams. You are given the effective speeds of a boat downstream (along the current) and upstream (against the current). From these, you can easily find the speed of the boat in still water and the speed of the current.

Given Data / Assumptions:

• Downstream speed (along the current) = 14 km/h.
• Upstream speed (against the current) = 7 km/h.
• Let b be the speed of the boat in still water.
• Let s be the speed of the stream.
• Then downstream speed = b + s, upstream speed = b - s.

Concept / Approach:
When downstream and upstream speeds are given, the speed of the boat in still water is simply the average of these two speeds. The current speed is half of their difference. This follows from solving the two simultaneous equations: b + s = downstream speed b - s = upstream speed Adding and subtracting these equations isolates b and s.

Step-by-Step Solution:
Step 1: Write the equations: b + s = 14 and b - s = 7. Step 2: Add the two equations: (b + s) + (b - s) = 14 + 7. Step 3: This gives 2b = 21, so b = 21 / 2 = 10.5 km/h. Step 4: If desired, we can also find the stream speed by subtracting: (b + s) - (b - s) = 14 - 7 ⇒ 2s = 7 ⇒ s = 3.5 km/h.

Verification / Alternative check:
Check that b = 10.5 and s = 3.5 fit both given speeds. Downstream speed = b + s = 10.5 + 3.5 = 14 km/h, which matches. Upstream speed = b - s = 10.5 - 3.5 = 7 km/h, which also matches the given value. Thus, the speed in still water is confirmed as 10.5 km/h.

Why Other Options Are Wrong:
Values like 3.5 or 14 km/h are actually the stream speed and downstream speed respectively, not the still water speed. Options 7.5 and 9.5 km/h do not satisfy the equations b + s = 14 and b - s = 7 for any real s. Only 10.5 km/h gives consistent upstream and downstream speeds.

Common Pitfalls:
Some learners mistakenly think the still water speed equals the downstream speed or confuse it with the stream speed. Others forget to divide by 2 after adding or subtracting the equations. Remember that still water speed is the average of upstream and downstream speeds, and always check your answer by substituting back into the original conditions.

Final Answer:
The speed of the boat in still water is 10.5 km/h.