A boat travels 30 km upstream and then 50 km downstream. Its speed in still water is 8 km/h and the speed of the current is 2 km/h. What is the average speed of the boat for the entire journey?
Answer
8 km/h
The correct answer is 8 km/h — Average speed = total distance ÷ total time = 80 km ÷ 10 h = 8 km/h.
Step-by-step solution
- Find effective upstream speed: 8 km/h – 2 km/h = 6 km/h.
- Find effective downstream speed: 8 km/h + 2 km/h = 10 km/h.
- Compute upstream travel time: 30 km ÷ 6 km/h = 5 hours.
- Compute downstream travel time: 50 km ÷ 10 km/h = 5 hours.
- Total distance = 30 km + 50 km = 80 km.
- Total time = 5 h + 5 h = 10 hours.
- Average speed = total distance ÷ total time = 80 km ÷ 10 h = 8 km/h.
Common mistake: Averaging the two speeds instead of using time-weighted average
Concept tested: Average speed with current in two directions
Published · How this solution was prepared and checked
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