Define Speeds in Terms of Stream Speed

Let the speed of the stream be $s\text{ km/h}$. The speed of the diver in still water is $3\text{ km/h}$. Therefore, upstream speed is $(3 - s)\text{ km/h}$ and downstream speed is $(3 + s)\text{ km/h}$.

$v_u = 3 - s, \quad v_d = 3 + s$

Set up the Time Equation

Distance is $50\text{ km}$. The time taken upstream is double the time taken downstream.

$\frac{50}{3 - s} = 2 \times \frac{50}{3 + s}$

Solve for Stream Speed ($s$)

Canceling $50$ from both sides gives $\frac{1}{3 - s} = \frac{2}{3 + s}$. Cross-multiplying yields $3 + s = 2(3 - s) \implies 3 + s = 6 - 2s \implies 3s = 3 \implies s = 1\text{ km/h}$.

$s = 1 \text{ km/h}$

Calculate Speed Against the Stream

Speed against the stream is the upstream speed: $3 - s = 3 - 1 = 2\text{ km/h}$.

$3 - 1 = 2 \text{ km/h}$