Mr. Arun rows a boat with the stream at 10 km/hr and against the stream in 5…
2017
Mr. Arun rows a boat with the stream at 10 km/hr and against the stream in 5 km/hr. In still water, his rate of rowing in km/h is:
- A.
7.5
- B.
2.5
- C.
5
- D.
15
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept
In boats-and-streams problems, two speeds are reported: the downstream speed (rowing with the current) and the upstream speed (rowing against the current). The boat's speed in still water is the average of these two, because rowing with the stream the current adds to the boat's own speed and rowing against it the current subtracts the same amount.
Speed in still water = (Downstream speed + Upstream speed) / 2.
Application
Downstream speed (with the stream) = 10 km/hr.
Upstream speed (against the stream) = 5 km/hr.
Speed in still water = (10 + 5) / 2 = 15 / 2 = 7.5 km/hr.
Cross-check
The speed of the stream itself = (Downstream - Upstream) / 2 = (10 - 5) / 2 = 2.5 km/hr. Adding the boat's still-water speed and the stream speed gives 7.5 + 2.5 = 10 km/hr (the downstream speed), and subtracting gives 7.5 - 2.5 = 5 km/hr (the upstream speed). Both match the given data, confirming the still-water speed is 7.5 km/hr.