The speed of a boat in still water is 10 Km/hr (10 Kmph). If it can travel 26…

Concept

For a boat moving with a stream, downstream speed equals still-water speed plus stream speed, while upstream speed equals still-water speed minus stream speed.

Time equals distance divided by speed. Equal travel times therefore give an equation between the downstream and upstream journeys.

Application

1. Let the stream speed be x km/h. Then the downstream speed is (10 + x) km/h and the upstream speed is (10 − x) km/h.

2. Since the travel times are equal, 26/(10 + x) = 14/(10 − x).

3. Cross-multiplication gives 26(10 − x) = 14(10 + x).

4. Expanding and solving gives 260 − 26x = 140 + 14x, so 120 = 40x and x = 3 km/h.

Cross-check

For x = 3, the downstream speed is 13 km/h and the upstream speed is 7 km/h. The times are 26/13 = 2 hours and 14/7 = 2 hours, so they are equal.

Therefore, the speed of the stream is 3 km/h.