Define Speeds in Terms of Stream Speed

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

$\text{Speed}_{\text{upstream}} = 3 - s, \quad \text{Speed}_{\text{downstream}} = 3 + s$

Set Up Time Equation

The distance for both upstream and downstream is $50\text{ km}$. According to the problem, 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 and cross-multiplying gives $3 + s = 2(3 - s)$, which simplifies to $3 + s = 6 - 2s$, leading to $3s = 3$ or $s = 1\text{ km/h}$.

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

Calculate Downstream Speed

Substitute the stream speed $s = 1\text{ km/h}$ into the downstream speed formula to find the final result.

$\text{Downstream Speed} = 3 + s = 3 + 1 = 4\text{ km/h}$