A boat goes 24 km upstream and 36 km downstream in 6 hours. It goes 36 km upstream and 24 km downstream in 6 hours 30 minutes. What is the speed of the stream?

Explanation

1. 01

   Let $x = \frac{1}{u}$ and $y = \frac{1}{d}$ for upstream and downstream speeds $u$, $d$.

2. 02

   $24x + 36y = 6$ and $36x + 24y = 6.5$.

3. 03

   Adding: $60(x + y) = 12.5$, so $x + y = \frac{5}{24}$. Subtracting: $12(x - y) = 0.5$, so $x - y = \frac{1}{24}$.

4. 04

   $x = \frac{1}{8}$, $y = \frac{1}{12}$: upstream 8 km/h, downstream 12 km/h.

5. 05

   Stream $= \frac{12 - 8}{2} = 2$ km/h.