The ratio of the speeds of Ferry X and Ferry Y in still water is 4 : 5, respectively. The speed of the river current is 10 km/h. Ferry X takes 3 hours to cover a distance of 150 km downstream. How long will it take Ferry Y to travel a distance of 240 km upstream?

The correct answer is 6 hours.

Step 1: Define the variables and given data

Let the speed of Ferry X in still water be $v_{\text{X}}$ and the speed of Ferry Y in still water be $v_{\text{Y}}$.

The ratio of their speeds in still water is given as:

$v_{\text{X}}$

The speed of the river current ($c$) is:

$c=10\text{km/h}$

Step 2: Find the speed of Ferry X in still water

Ferry X covers a downstream distance of $150\text{km}$ in $3\text{hours}$.

The downstream speed of Ferry X is calculated using the formula:

$\text{Downstream Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{Downstream Speed of Ferry X}=\frac{150\text{km}}{3\text{hours}}=50\text{km/h}$

Since downstream speed equals the speed of the ferry in still water plus the stream speed:

$v_{\text{X}}$

$v_{\text{X}}$

$v_{\text{X}}$

Step 3: Calculate the speed of Ferry Y in still water

Using the speed ratio $v_{\text{X}}$, we have:

$v_{\text{Y}}$

Substitute $v_{\text{X}}$:

$v_{\text{Y}}$

Step 4: Calculate the upstream speed of Ferry Y

Upstream speed equals the speed in still water minus the stream speed:

$\text{Upstream Speed of Ferry Y}=v_{\text{Y}}$

$\text{Upstream Speed of Ferry Y}=50-10=40\text{km/h}$

Step 5: Calculate the time required for Ferry Y to travel 240 km upstream

$\text{Time}=\frac{\text{Distance}}{\text{Upstream Speed}}$

$\text{Time}=\frac{240\text{km}}{40\text{km/h}}=6\text{hours}$

Therefore, it will take Ferry Y 6 hours to travel a distance of 240 km upstream.