Mr. Vijay rows a boat with the stream at 8 km/hr and against the stream at 4…
2017
Mr. Vijay rows a boat with the stream at 8 km/hr and against the stream at 4 km/hr. In still water, his rate of rowing in km/hr is:
- A.
4 km/h
- B.
2 km/h
- C.
3 km/h
- D.
6 km/h
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Concept
When a boat travels in a stream, its observed speed is the boat's still-water speed adjusted by the stream's speed. Downstream the stream adds to it, upstream it subtracts. So the still-water speed is the average of the downstream and upstream speeds: still water = (downstream + upstream) / 2.
Application
Downstream speed (with the stream) = 8 km/hr; upstream speed (against the stream) = 4 km/hr.
Still-water speed = (downstream + upstream) / 2 = (8 + 4) / 2.
= 12 / 2 = 6 km/hr.
Cross-check
From the same pair, the stream's speed = (downstream - upstream) / 2 = (8 - 4) / 2 = 2 km/hr. Adding it back: still water + stream = 6 + 2 = 8 = downstream, and still water - stream = 6 - 2 = 4 = upstream. Both match, confirming the still-water rate is 6 km/hr.