In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the…
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In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
- A.
3 km/hr
- B.
5 km/hr
- C.
8 km/hr
- D.
9 km/hr
Attempted by 1 students.
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Correct answer: C
A boat's downstream speed equals its own speed in still water plus the stream's speed, and its upstream speed equals its own speed minus the stream's speed. Adding the two cancels the stream's speed, so the boat's speed in still water is simply half the sum of the downstream and upstream speeds.
Downstream speed = 11 km/hr, Upstream speed = 5 km/hr (given).
Boat's speed in still water = (Downstream speed + Upstream speed) / 2 = (11 + 5) / 2.
(11 + 5) / 2 = 16 / 2 = 8 km/hr.
Cross-check: the stream's speed = (Downstream speed − Upstream speed) / 2 = (11 − 5) / 2 = 3 km/hr. Adding this to the boat's speed gives 8 + 3 = 11 km/hr (matches the downstream speed), and subtracting gives 8 − 3 = 5 km/hr (matches the upstream speed) — confirming the boat's speed in still water is 8 km/hr.