This problem involves the concept of boats and streams, where the speed of the boat is affected by the speed of the water current.

When a boat travels upstream, it goes against the current, so its effective speed (upstream speed) is the speed of the boat in still water minus the speed of the stream.

When a boat travels downstream, it goes with the current, so its effective speed (downstream speed) is the speed of the boat in still water plus the speed of the stream.

Let:

• \(V_b\) = Speed of the boat in still water (in km/hr)
• \(V_s\) = Speed of the stream (in km/hr)

Then:

• Upstream Speed (\(V_u\)) = \(V_b - V_s\)
• Downstream Speed (\(V_d\)) = \(V_b + V_s\)

We are given the following information:

• Distance covered upstream = 30 km
• Time taken upstream = 3 hours
• Distance covered downstream = 30 km
• Time taken downstream = 1 hour

We can calculate the upstream and downstream speeds using the formula: Speed = Distance / Time.

Calculating Upstream and Downstream Speeds

Upstream Speed:

\[V_u = \frac{\text{Distance Upstream}}{\text{Time Upstream}}\]

\[V_u = \frac{30 \text{ km}}{3 \text{ hours}} = 10 \text{ km/hr}\]

So, \(V_b - V_s = 10\) km/hr. Let's call this Equation (1).

Downstream Speed:

\[V_d = \frac{\text{Distance Downstream}}{\text{Time Downstream}}\]

\[V_d = \frac{30 \text{ km}}{1 \text{ hour}} = 30 \text{ km/hr}\]

So, \(V_b + V_s = 30\) km/hr. Let's call this Equation (2).

Finding the Speed of the Boat in Still Water

We have a system of two linear equations:

Equation (1): \(V_b - V_s = 10\)

Equation (2): \(V_b + V_s = 30\)

To find \(V_b\), we can add Equation (1) and Equation (2):

\[(V_b - V_s) + (V_b + V_s) = 10 + 30\]

\[V_b - V_s + V_b + V_s = 40\]

\[2V_b = 40\]

\[V_b = \frac{40}{2} = 20 \text{ km/hr}\]

The speed of the boat in still water is 20 km/hr.

Alternatively, the speed of the boat in still water can be directly calculated as the average of the downstream and upstream speeds:

\[V_b = \frac{V_d + V_u}{2}\]

\[V_b = \frac{30 \text{ km/hr} + 10 \text{ km/hr}}{2} = \frac{40 \text{ km/hr}}{2} = 20 \text{ km/hr}\]

Calculating Time to Cover 60 km in Still Water

We need to find the time taken by the boat to cover a distance of 60 km in still water.

• Distance = 60 km
• Speed (in still water) = \(V_b = 20\) km/hr

Using the formula: Time = Distance / Speed

\[\text{Time} = \frac{60 \text{ km}}{20 \text{ km/hr}}\]

\[\text{Time} = 3 \text{ hours}\]

The boat will take 3 hours to cover 60 km in still water.

Let's check the options provided:

Our calculated time is 3 hours, which matches Option 1.

Revision Table: Boat and Stream Concepts

Additional Information: Solving Boat and Stream Problems

Boat and stream problems are common in quantitative aptitude. They typically involve understanding the relationship between the boat's speed, the stream's speed, and the resulting effective speeds when moving upstream or downstream.

Key steps usually involve:

• Defining variables for the speed of the boat in still water and the speed of the stream.
• Setting up equations based on the given information about upstream and downstream travel (distance and time). Remember, distance = speed × time.
• Solving the system of equations to find the unknown speeds (\(V_b\) and/or \(V_s\)).
• Using the calculated speeds to find the answer to the specific question asked, often involving time, distance, or speed in a different scenario (like still water).

It's important to correctly identify whether the boat is moving upstream or downstream as this determines whether the stream's speed is subtracted from or added to the boat's speed in still water.

This problem specifically asked for the time taken in still water, which required us to first find the boat's speed in still water using the upstream and downstream data.