Solving Time and Distance Problems for Boats in Still Water

Solving problems involving boats moving in water can be a bit tricky, but with a clear understanding of the concepts, the process becomes more straightforward. In this article, we'll explore how to calculate the time taken by a boat to travel a certain distance in still water, given the upstream and downstream speeds. We'll use several examples to demonstrate the methodology.

Example 1

A boat goes 24 km upstream in 3 hours and downstream in 2 hours. What amount of time will this boat take to travel 60 km in all still water?

Solution:

First, we calculate the speeds upstream and downstream.

Speed upstream 24 km/3 hrs 8 km/hr Speed downstream 24 km/2 hrs 12 km/hr

The speed in still water can be calculated by averaging the upstream and downstream speeds:

Still water speed (12 km/hr 8 km/hr) / 2 10 km/hr

To find the time taken to travel 60 km in still water:

Time Distance / Speed 60 km / 10 km/hr 6 hours

Explanation:

The key here is to understand that the still water speed is the average of the upstream and downstream speeds.

Related Formula: Speed in still water (Speed downstream Speed upstream) / 2

Example 2

A boat goes 20 km upstream in 2 hours and downstream in 1 hour. How much time will this boat take to travel 80 km in still water?

Solution:

Speed upstream 20 km/2 hrs 10 km/hr Speed downstream 20 km/1 hr 20 km/hr

Calculate the speed in still water:

Still water speed (20 km/hr 10 km/hr) / 2 15 km/hr

Time in still water:

Time Distance / Speed 80 km / 15 km/hr 5.33 hours ≈ 5 hours 20 minutes

Explanation:

Again, the still water speed is the average of the upstream and downstream speeds. The time can then be calculated using the standard distance/speed formula.

General Formula

The general formula for the speed in still water is:

Speed in still water (Speed downstream Speed upstream) / 2

The time taken in still water can be calculated as:

Time Distance / Speed in still water

Conclusion

Understanding how to solve these types of problems is crucial for competitive exams as well as real-world scenarios. By breaking down the problem into simpler steps, we can easily find the required time in still water.

Keywords:

boat speed in still water, upstream and downstream, time and distance

Useful Links:

To understand more about boat and stream questions, refer to:

What are some formulas and tricks to solve boat and stream questions in a competitive exam? Khan Academy: Boat Problems