How Helen’s Walking Pattern Affects Her Final Position

Imagine a scenario where Helen takes 1 step forward and 2 steps backward every 10 seconds. Over a span of 30 minutes, how many steps will she have walked, and in which direction? This article will guide you through the step-by-step calculation and explain the underlying logic.

Solving the Problem

To solve the problem, let's break it down into manageable steps:

1. Determine the Total Time in Seconds

First, we need to calculate the total time in seconds. Given that there are 30 minutes:

n - 30 minutes 30 × 60 seconds 1800 seconds

2. Determine the Number of Cycles in 10 Seconds

Each cycle consists of:

1 step forward 2 steps backward

Given that one cycle takes 10 seconds, we determine the number of cycles in 1800 seconds:

n - The number of cycles in 1800 seconds 1800 seconds ÷ 10 seconds/cycle 180 cycles

3. Calculate the Total Steps Taken

In each cycle, Helen's net movement is:

n - 1 step forward 2 steps backward

Given 180 cycles, the total steps taken are:

Forward steps 1 step/cycle × 180 cycles 180 steps forward Backward steps 2 steps/cycle × 180 cycles 360 steps backward

4. Determine the Net Steps

Calculating the net steps:

n - Total steps Forward steps - Backward steps 180 - 360 -180 steps

Conclusion

Therefore, in 30 minutes, Helen will have taken 180 steps backward. This means that despite taking more steps, her net progress is negative due to the overlapping steps backward.

Additional Insights

In another related scenario, consider a man who takes 1 step forward and 2 steps backward every 10 seconds. Similarly, this person would take 1 step backward every 10 seconds. Over 30 minutes (1800 seconds), the total steps backward would be:

1800 seconds ÷ 10 seconds 180 steps back

In both scenarios, the key lies in understanding the net effect of the steps taken over time.

Understanding Step Movements

Let's break down the step movements for a clearer understanding:

Steps and Distance: In the context of walking, a 'step' is a unit of measurement for distance covered during movement. Each 'step' involves moving the foot forward, backward, sideways, or diagonally. Backward Steps: The term 'backward steps' denotes movement in a reverse direction relative to the intended path.

This article provides a comprehensive guide to solving such problems and offers insight into how to navigate similar scenarios involving multiple movements in different directions.