Calculating Distance Walked: A Comprehensive Guide
Have you ever wondered how far you walked given certain conditions? Let's explore a fun problem and break it down step-by-step to ensure a clear understanding of distance calculations, including the impact of pauses during your journey.
Understanding the Problem
The problem at hand involves a person who walks at a constant speed of 4 miles per hour (mph) for a total of 2 hours, but stops walking for 20 minutes. Our task is to determine how far the person actually walked, taking into account the time spent not moving.
Step-by-Step Calculation: No Pauses
Let's start with the scenario where there are no pauses. The formula for distance (s) is:
s u times; t
Where:
s is the distance. u is the speed. t is the time.Given:
u 4 mph (constant speed). t 2 hours.Since there are no pauses, calculate the total distance as follows:
s 4 mph times; 2 hours 8 miles
Step-by-Step Calculation: Including Pauses
Now, let's incorporate the 20-minute pause into the calculation. Here's how to approach it step-by-step:
Convert the pause time from minutes to hours: 20 minutes 20/60 hours 1/3 hours. Calculate the actual time spent walking: 2 hours - 1/3 hours 5/3 hours or 1 hour 40 minutes. Apply the distance formula again: s 4 mph times; 5/3 hours 20/3 miles Convert the result to a mixed number: 20/3 miles 6 2/3 miles, which is approximately 6.67 miles (considering 2/3 of a mile is 1173 yards and 1 foot).Understanding the Question Statement
The question provided multiple perspectives, and understanding the nuances is crucial.
Solution 1: Considering the Pause
One solution suggests a distance of 6.68 miles, derived from the calculation of:
s 4 mph times; (2 - 1/3) hours 6.666 miles ≈ 6.68 miles
Solution 2: No Changes Due to Pauses
Another perspective states that the 20-minute pause does not affect the total distance walked, as the total walking time is still considered the full 2 hours of the journey.
The total distance walked, without considering the pause, remains 8 miles.
Conclusion
Understanding the difference between distance walked and total journey distance is key. In scenarios where pauses are considered, the distance walked would be less, taking into account the time spent not walking. However, if the focus is on the total journey covered, including walking and pauses, then the full 8 miles are considered.
For those interested in more in-depth discussions on distance calculations and other related topics, explore further resources online or consult with professionals in the field of physics and mathematics.