In one hour the boat covers 11 km with the current and 5 km against it. What is the speed of the boat in still water (km/h)?

Given data

• Downstream speed = 11 km/h
• Upstream speed = 5 km/h

Concept / Approach

• Let u be still-water speed and v be current speed. Then u + v = 11 and u − v = 5.
• Adding the two gives u.

Step-by-step calculation

u = ( (u + v) + (u − v) ) / 2 = (11 + 5)/2 = 8 km/h

Verification

v = (11 − 5)/2 = 3 km/h. Then downstream = 8 + 3 = 11, upstream = 8 − 3 = 5.

Common pitfalls

• Taking a simple average of distances rather than speeds; here we directly average the given speeds to find u.

Final Answer

8 km/h