A boat takes 6 hours to cover 36 km downstream and 8 hours to cover 32 km…
2023
A boat takes 6 hours to cover 36 km downstream and 8 hours to cover 32 km upstream. Then the speed of the boat in still water is?
- A.
3 km/h
- B.
4 km/h
- C.
5 km/h
- D.
6 km/h
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept: For a boat moving in a stream, the downstream speed equals the boat's speed plus the stream's speed, and the upstream speed equals the boat's speed minus the stream's speed. Adding the two legs cancels the stream's contribution, so the boat's own speed in still water is the average of the downstream and upstream speeds.
Downstream speed = distance ÷ time = 36 km ÷ 6 h = 6 km/h.
Upstream speed = distance ÷ time = 32 km ÷ 8 h = 4 km/h.
Speed of the boat in still water = (downstream speed + upstream speed) ÷ 2 = (6 + 4) ÷ 2 = 5 km/h.
Cross-check: stream speed = (downstream − upstream) ÷ 2 = (6 − 4) ÷ 2 = 1 km/h. Then boat + stream = 5 + 1 = 6 km/h (matches the downstream leg) and boat − stream = 5 − 1 = 4 km/h (matches the upstream leg), confirming the result.
