Question

A boat covers 24 km upstream and 72 km downstream in 8 hours, while it covers 48 km upstream and 108 km downstream in 14 hours. Find the speed of the boat in still water and the speed of the stream respectively.

Accepted Answer

A. Let upstream speed be $u$ and downstream speed be $v$. $$\frac{24}{u} + \frac{72}{v} = 8$$ $$\frac{48}{u} + \frac{108}{v} = 14$$ Multiplying the first equation by 2: $$\frac{48}{u} + \frac{144}{v} = 16$$ Subtracting the second equation: $$\frac{36}{v} = 2 \implies v = 18	ext{ km/h.}$$ Substitute $v = 18$ into first equation: $$\frac{24}{u} + 4 = 8 \implies u = 6	ext{ km/h.}$$ Speed of boat in still water = $\frac{18 + 6}{2} = 12$ km/h. Speed of stream = $\frac{18 - 6}{2} = 6$ km/h.

Upstream and downstream boat speed

Explanation

Practise this under exam conditions