Ratio of the downstream speed of boat to the upstream speed of boat is 3: 1 and the time taken by a boat to cover 144 km in downstream is 8 hours. Find the time taken by the boat to cover same distance in still water.

The correct answer is 12 hours.

Let us break down the solution step-by-step:

Step 1: Understand the given variables and ratios
Let the downstream speed of the boat be $D_s$ and the upstream speed of the boat be $U_s$.
We are given that the ratio of the downstream speed to the upstream speed is 3:1.
Therefore, we can write:
$D_s=3x$
$U_s=x$
where $x$ is a common constant multiplier.

Step 2: Calculate the downstream speed
We are given that the boat takes 8 hours to cover a distance of 144 km downstream.
Using the speed formula, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$:
$D_s=\frac{144}{8}=18\text{km/h}$

Step 3: Find the value of x and the upstream speed
Since $D_s=3x=18\text{km/h}$, we can solve for $x$:
$x=\frac{18}{3}=6\text{km/h}$
Thus, the upstream speed is:
$U_s=x=6\text{km/h}$

Step 4: Find the speed of the boat in still water
The speed of a boat in still water (let's call it $B_s$) is the average of its downstream speed and upstream speed:
$B_s=\frac{D_s+U_s}{2}$
Substituting the values we found:
$B_s=\frac{18+6}{2}=\frac{24}{2}=12\text{km/h}$

Step 5: Find the time taken to cover the same distance in still water
The distance to be covered in still water is the same, which is 144 km.
Using the time formula, $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:
$\text{Time}=\frac{144}{12}=12\text{hours}$

Therefore, the time taken by the boat to cover the same distance in still water is 12 hours.