A ferry takes 90 minutes to travel a specific distance while moving downstream along a river. Provided that the speed of the ferry in calm water and the speed of the current are in the ratio of 3: 1, calculate the time required for the ferry to travel the exact same distance upstream.

Correct Answer: 3 hours

Step-by-Step Explanation:

1. Understand Downstream and Upstream Speeds

When a vessel moves downstream, it travels in the direction of the river's flow. Thus, the effective downstream speed is the sum of the speed of the ferry in calm water and the speed of the stream current.
When traveling upstream, the vessel moves against the direction of the river's flow. Thus, the effective upstream speed is the difference between the speed of the ferry in calm water and the speed of the stream current.

2. Express the Speeds using the Given Ratio

The ratio of the speed of the ferry in calm water to the speed of the river current is given as 3 : 1.

Let the speed of the current be $x$.

Then, the speed of the ferry in calm water is $3x$.

Now, calculate the downstream speed:

$\text{Downstream speed}=3x+x=4x$

Next, calculate the upstream speed:

$\text{Upstream speed}=3x-x=2x$

3. Calculate the Distance Covered Downstream

The ferry takes 90 minutes to travel downstream. Convert this duration into hours:

$\text{Time downstream}=\frac{90}{60}=1.5\text{hours}$

Using the distance formula $\text{Distance}=\text{Speed}\times \text{Time}$:

$\text{Distance}=4x\times 1.5=6x$

4. Calculate the Time Needed to Travel Upstream

The ferry travels the exact same distance ($6x$) upstream at an upstream speed of $2x$.

Using the time formula $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

$\text{Time upstream}=\frac{6x}{2x}=3\text{hours}$

Therefore, the time required for the ferry to travel the same distance upstream is 3 hours.