A boat can row 36 km downstream in the same time as it takes to row 24 km upstream. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

The correct option is 15 km/h.

Step-by-step Explanation:

1. Understand the given data:

Let the speed of the boat in still water be v km/h.

The speed of the stream is given as s = 3 km/h.

2. Formulate speeds for downstream and upstream:

When traveling downstream, the stream assists the boat:

Speed downstream (v_d) = v + 3 km/h

When traveling upstream, the stream opposes the boat:

Speed upstream (v_u) = v - 3 km/h

3. Set up the equation using time:

We know that Time = Distance / Speed.

The problem states that the time taken to cover 36 km downstream is equal to the time taken to cover 24 km upstream.

$\frac{36}{v+3}=\frac{24}{v-3}$

4. Solve for v:

Simplify the fraction ratio by dividing both numerators by 12:

$\frac{3}{v+3}=\frac{2}{v-3}$

Cross-multiply to solve the equation:

$3(v-3)=2(v+3)$

$3v-9=2v+6$

$3v-2v=6+9$

$v=15$

Therefore, the speed of the boat in still water is 15 km/h.