Calculating Time to Cover a Distance with Periodic Rests: A Detailed Guide

In our daily lives, we often encounter situations where we need to cover a certain distance while periodically taking rests. This can be crucial, especially in physical activities where rest is vital. Let's explore a practical scenario: A man walking at a speed of 18 kilometers per hour, taking a rest for 18 minutes after each kilometer, aims to cover a total distance of 54 kilometers. How long will it take him to reach his destination? We will walk through the calculation step-by-step to provide a comprehensive solution.

Step-by-Step Calculation

Let's break down the problem into two main parts: the walking time and the resting time.

Step 1: Calculate the Walking Time

The walking speed is given as 18 kilometers per hour. To calculate the time taken to walk a specific distance, we use the formula:

Time Distance / Speed

For a distance of 54 kilometers, the walking time can be calculated as:

Walking Time 54 km / 18 km/hour 3 hours

Step 2: Calculate the Resting Time

The man takes a 18-minute rest after every kilometer, except for the last kilometer. Given that he needs to cover 54 kilometers, he will have 53 intervals in which he takes a rest.

The number of rests is 53. Therefore, the total resting time is:

Resting Time Number of rests x Resting time per rest

Resting Time 53 x 18 minutes

First, let's convert the rest time from minutes to hours:

18 minutes 18 / 60 hours 0.3 hours

Now, calculate the total resting time in hours:

Resting Time 53 x 0.3 hours 15.9 hours

Step 3: Calculate the Total Time

To find the total time taken, we add the walking time and the resting time:

Total Time Walking Time Resting Time 3 hours 15.9 hours 18.9 hours

Step 4: Convert Total Time into Hours and Minutes

To convert 0.9 hours into minutes:

0.9 hours x 60 minutes/hour 54 minutes

Therefore, the total time taken is:

18 hours 54 minutes 18 hours and 54 minutes

Final Answer: 18 hours 54 minutes

Optimization of Walking and Resting Time

The above calculation shows us how to determine the exact time required when walking at a constant speed and taking rests at specific intervals. This example highlights the importance of balancing work and rest, ensuring that the effort is managed efficiently to achieve the desired results.

Conclusion

While it is crucial to cover distances efficiently, it is equally important to balance the journey with appropriate rest periods. In the given scenario, the man will need 18 hours and 54 minutes to cover 54 kilometers, considering he stops for 18 minutes every kilometer. Understanding and managing such scenarios can be beneficial in various fields, from sports and fitness to logistics and transportation.

References

For a deeper understanding of time management and distance calculations, consider exploring additional resources on mathematics and physics, particularly those related to speed, distance, and time calculations.