A man can row $7.5\text{km}$ an hour in still water. He finds that it takes four times as much time to row upstream as it takes to row downstream. The speed of the stream is:

Let the speed of the man in still water be $u=7.5\text{km/h}$ and the speed of the stream be $v\text{km/h}$.
* Downstream speed ($v_{\text{down}}$) = $u+v=7.5+v$
* Upstream speed ($v_{\text{up}}$) = $u-v=7.5-v$

According to the question, the time taken to row upstream is four times the time taken to row downstream for the same distance ($d$):

$$t_{\text{up}}=4\times t_{\text{down}}$$

$$\frac{d}{u-v}=4\times \frac{d}{u+v}$$

$$u+v=4(u-v)$$

$$u+v=4u-4v$$

$$5v=3u$$

Substitute the value of $u=7.5\text{km/h}$:

$$5v=3\times 7.5$$

$$5v=22.5$$

$$v=\frac{22.5}{5}=4.5\text{km/h}$$

Therefore, the speed of the stream is $4.5\text{km/h}$.