A man can row upstream at 16 km/h and downstream at 24 km/h. What is the speed of the current (in km/h)?

Introduction / Context:
This is a direct application of the basic formulas for boats and streams. You are given upstream and downstream speeds, and you must find the speed of the current using simple averages and differences. It checks that you know the essential relationships between these quantities.

Given Data / Assumptions:
- Upstream speed = 16 km/h. - Downstream speed = 24 km/h. - Let b be the speed of the boat in still water (km/h). - Let c be the speed of the current (km/h). - Upstream speed = b - c, downstream speed = b + c.

Concept / Approach:
Because upstream speed is boat speed minus current speed and downstream speed is boat speed plus current speed, we can obtain b and c by solving the two equations. The current speed is half of the difference between downstream and upstream speeds, while the still water speed is their simple average.

Step-by-Step Solution:
Step 1: b + c = 24 (downstream). Step 2: b - c = 16 (upstream). Step 3: Subtract the upstream equation from the downstream equation: (b + c) - (b - c) = 24 - 16. Step 4: This gives 2c = 8. Step 5: Therefore c = 8 / 2 = 4 km/h.

Verification / Alternative check:
You can also use the shortcut formula for current speed: c = (downstream speed - upstream speed) / 2. Here that is c = (24 - 16) / 2 = 8 / 2 = 4 km/h. Using b = (24 + 16) / 2 = 20 km/h gives upstream speed = 20 - 4 = 16 km/h and downstream speed = 20 + 4 = 24 km/h, exactly as given.

Why Other Options Are Wrong:
- 6 km/h or 5 km/h would not give the correct upstream and downstream speeds when combined with the implied boat speed. - 3 km/h and 8 km/h are not equal to half the difference between 24 and 16.

Common Pitfalls:
Learners sometimes average the two speeds incorrectly or think that the current equals the smaller speed. Others forget that the current affects both directions and that the difference between downstream and upstream speeds is twice the current. Remember the simple formulas: b = (downstream + upstream) / 2 and c = (downstream - upstream) / 2.

Final Answer:
The speed of the current is 4 km/h.