Ashu can row 7.5 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:

The correct answer is 4.5 km/h.

Step 1: Identify the given information

Speed of Ashu in still water (let this be $u$) = 7.5 km/h.
Let the speed of the stream be $v$ km/h.

Step 2: Express upstream and downstream speeds

When rowing downstream (in the direction of the stream), the effective speed is the sum of the speed in still water and the speed of the stream:
$\text{Downstream speed (}{d}_{\text{speed}}\text{)}=(u+v)=(7.5+v)\text{km/h}$

When rowing upstream (against the direction of the stream), the effective speed is the difference between the speed in still water and the speed of the stream:
$\text{Upstream speed (}{u}_{\text{speed}}\text{)}=(u-v)=(7.5-v)\text{km/h}$

Step 3: Set up the relationship between time and speed

For a fixed distance $D$, the time taken is inversely proportional to speed ($\text{Time}=\frac{D}{\text{Speed}}$).

According to the question, the time taken to row upstream is four times the time taken to row downstream:
$t_{\text{upstream}}=4\×t_{\text{downstream}}$

Since distance $D$ is constant:
$\frac{D}{7.5-v}=4\×\frac{D}{7.5+v}$

Canceling $D$ from both sides gives:
$7.5+v=4\×(7.5-v)$

Step 4: Solve for $v$

Expanding the equation:
$7.5+v=30-4v$

Rearranging the terms to group $v$ on one side:
$v+4v=30-7.5$

$5v=22.5$

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

Thus, the speed of the stream is 4.5 km/h.