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When dealing with mean calculation, it helps to first understand what 'mean' actually means. The mean is essentially the average of a set of numbers.
To find this, you simply add up all the numbers and then divide by the total count of numbers. In this problem, we initially had three team members whose combined lap time was 159 seconds, which results in a mean lap time of 53 seconds for them. By setting the overall mean desired at 50 seconds for all five members, we then calculate backwards to see what the remaining two members' mean time would need to be. Here’s a simple walkthrough:

• First three team members: total time, 159 seconds; mean time per person, 53 seconds.
• Overall desired mean for all five: 50 seconds per person.
• Adjust the total time calculation to achieve this mean with five participants.

This backward calculation is key when you have specific mean requirements and partial initial data.

Developing effective problem solving skills starts with breaking down a problem into manageable steps. In this scenario, we identified the initial situation (the mean time of the first three members) and the desired outcome (an overall team mean of 50 seconds).
We then used logical reasoning to find what's missing - in this case, the mean time needed for the remaining two team members. Here are some vital strategies to strengthen your problem solving skills:

• Identify what you know and what you need to find out. This clarifies the problem's scope.
• Work step-by-step to avoid skipping crucial elements.
• Check your work as you progress, ensuring each part builds on the last correctly.

By practicing these methods, you create a road map that leads you to a successful solution. Such structured approaches are universally applicable, from math problems to real-world challenges.

Setting up equations correctly is crucial for resolving mathematical problems. In this case, we used an equation to represent the overall mean lap time for the stilt-walking relay team.
Here's how you can set it up and solve such equations efficiently. Understanding the problem's structure helps in forming accurate equations:

• Always define what each element of the equation represents—here, the 250 seconds is the result of multiplying the desired mean (50 seconds) by five runners.
• Calculate known variables first; we calculated the time the first three runners took (159 seconds).
• Use the equation to find unknowns—in our task, this was the combined time for the last two runners (250 - 159 = 91 seconds).

Ultimately, forming equations involves translating what's happening in words into mathematical terms. Once you become familiar with setting up and solving equations, you can tackle a wide array of problems with confidence.