A man can row upstream at 24 km/hr. And downstream at 30 km/hr. Find the speed of the current.7 km/hr.3 km/hr.9 km/hr.6 km/hr

1. Break Down the Problem

To find the speed of the current, we need to identify the speed of the man rowing upstream and downstream, and then relate these speeds to the speed of the current.

Let:

• $u$ = speed of the man in still water
• $v$ = speed of the current

From the problem:

• Upstream speed (against the current) = $u - v = 24$ km/hr
• Downstream speed (with the current) = $u + v = 30$ km/hr

2. Relevant Concepts

We can use these two equations to solve for the speed of the current $v$:

1. $u - v = 24$
2. $u + v = 30$

3. Analysis and Detail

To find $u$ and $v$, we can add the two equations:

$(u - v) + (u + v) = 24 + 30$

This simplifies to:

$2u = 54 \quad \Rightarrow \quad u = \frac{54}{2} = 27 \text{ km/hr}$

Now, substitute $u = 27$ back into either equation to find $v$. Using the first equation:

$27 - v = 24$

Solving for $v$:

$v = 27 - 24 = 3 \text{ km/hr}$

4. Verify and Summarize

Now we verify the findings:

• Upstream speed: $27 - 3 = 24$ km/hr (correct)
• Downstream speed: $27 + 3 = 30$ km/hr (correct)

Thus, the calculations are consistent.

Final Answer

The speed of the current is $\boxed{3}$ km/hr.