The problem asks to determine the speed of the stream given the following:

• Swati rows a boat at a speed of 5 km/h in still water.
• It takes her one hour more to row the boat 5.25 km upstream than downstream.

Let:

• $x$ = speed of the stream in km/h.

When rowing upstream, the effective speed is $5 - x$ km/h, since the current slows her down. The time to row upstream is given by: $t_{\text{upstream}} = \frac{5.25}{5 - x}$

When rowing downstream, the effective speed is $5 + x$ km/h, since the current aids her. The time to row downstream is given by: $t_{\text{downstream}} = \frac{5.25}{5 + x}$

It is also given that the upstream journey takes 1 hour longer than the downstream journey: $t_{\text{upstream}} = t_{\text{downstream}} + 1$

Substitute the expressions for time into this equation: $\frac{5.25}{5 - x} = \frac{5.25}{5 + x} + 1$

Now, let's solve this equation.The two solutions for the speed of the stream are $x = -12.5$ km/h and $x = 2$ km/h. Since a negative speed does not make physical sense in this context, the valid solution is:

$x = 2 \, \text{km/h}$

Thus, the speed of the stream is 2 km/h.

Would you like further details on this solution, or do you have any questions?

Related Questions:

1. What would happen if the speed of the boat in still water were changed?
2. How would the time difference change if the distance were longer than 5.25 km?
3. What is the effect of stream speed on upstream and downstream times?
4. How do you solve for the stream speed when both the boat speed and time difference are unknown?
5. Can this method be applied to distances other than 5.25 km?

Tip:

Always ensure that physical quantities like speed are positive when solving real-world problems.