The speed of a boat downstream is 14 km/h and upstream is 8 km/h. What is the speed (in km/h) of the current?

Introduction / Context:
This question again uses the basic boats-and-streams model. You are given the effective speeds with and against the current and are asked to find the speed of the current alone.

Given Data / Assumptions:
• Downstream speed = 14 km/h.• Upstream speed = 8 km/h.• Let boat speed in still water = u km/h.• Let stream speed = v km/h.

Concept / Approach:
The standard relations are: downstream speed = u + v and upstream speed = u − v. Adding them gives 2u; subtracting them gives 2v. The stream speed is therefore half the difference between downstream and upstream speeds.

Step-by-Step Solution:
Step 1: Write equations: u + v = 14 and u − v = 8.Step 2: Subtract the second from the first: (u + v) − (u − v) = 14 − 8.Step 3: This simplifies to 2v = 6.Step 4: So v = 6 ÷ 2 = 3 km/h.

Verification / Alternative check:
Using v = 3, we can quickly find u. Substitute into u − v = 8 ⇒ u − 3 = 8 ⇒ u = 11 km/h. Check downstream: u + v = 11 + 3 = 14 km/h, which matches the given value, confirming v = 3 km/h is correct.

Why Other Options Are Wrong:
11 kms/hr: This is the boat's own speed in still water, not the stream speed.6 kms/hr: Equal to the full difference (14 − 8), but the stream speed is half this difference.5.5 kms/hr: A random average-like value that does not fit the equations.

Common Pitfalls:
The usual mistake is to take the difference of speeds (14 − 8 = 6) as the stream speed directly. Remember that the difference equals 2v, so you must divide by 2 to get the current's velocity.

Final Answer:
The speed of the current is 3 km/h.