Calculate Raju's Still Water Speed

Let $s$ represent Raju's speed in still water (in km/h) and $r$ represent the speed of the river flow (in km/h).

Determine Speeds

• The speed when rowing downstream is Raju's speed plus the river's speed: $v_{down} = s + r$.
• The speed when rowing upstream is Raju's speed minus the river's speed: $v_{up} = s - r$.

Use Given Information

• The river flows at $r = 5\text{ km/h}$.
• Raju takes twice as long to row upstream as downstream. Let $t_{up}$ be the time taken upstream and $t_{down}$ be the time taken downstream. This means $t_{up} = 2 \times t_{down}$.

Relate Speeds and Time

Since time = distance / speed, and assuming the distance rowed upstream and downstream is the same ($d$), we have:

• $t_{up} = \frac{d}{v_{up}}$
• $t_{down} = \frac{d}{v_{down}}$

Substituting these into the time relationship ($t_{up} = 2 \times t_{down}$):

Canceling the distance $d$ from both sides gives the relationship between the speeds:

This implies:

Solve for Raju's Speed

Now substitute the expressions for $v_{down}$ and $v_{up}$:

Expand the equation:

Rearrange the terms to solve for $s$:

Substitute the given river speed ($r = 5\text{ km/h}$):

Therefore, Raju's speed in still water is $15\text{ km/h}$.