Math Problem Statement

Nemo Sum walks from point A to point B and then back again, taking the exact same path in the opposite direction. Nemo always walks in one of the cardinal directions, i.e. north, south, east, or west, but not always at the same speed. For reasons known only to higher powers, Nemo always walks at 4 km/h when going North or South; going East, Nemo always walks at 3 km/h; and going West, Nemo always walks at 6 km/h.

Solution

To address this scenario, let’s summarize the key details about Nemo's walk:

  • Speed going North or South: 4 km/h
  • Speed going East: 3 km/h
  • Speed going West: 6 km/h

Nemo follows a path from point A to point B and back again, so he covers the same distance twice (once in each direction). The challenge is that Nemo's speed depends on the cardinal direction of travel.

General Strategy for Problem Solving:

  1. Path Composition: We need to know the specific breakdown of the distances Nemo travels in each direction (North, South, East, and West).
  2. Time Calculation: The time it takes Nemo to travel along a segment of the path in each direction depends on both the distance traveled and his speed in that direction. Time is calculated as: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}
  3. Total Time: To compute Nemo's total travel time, we sum up the time taken for each segment (both on the way to point B and on the return to point A).

Required Information:

To move forward, we need:

  • The exact distances that Nemo walks in each cardinal direction (North, South, East, West).

Once we have this, we can calculate Nemo's total travel time in both directions. Would you like to specify those details or provide more information about the path Nemo took?


Next Steps:

  1. What is the total distance Nemo travels in each direction?
  2. Does Nemo walk equal distances going North and South, and East and West?
  3. Is Nemo's path a straight line or a combination of segments?
  4. What is the total time it takes for Nemo to walk the entire journey?
  5. How does Nemo’s speed affect the total travel time?

Tip: To calculate time effectively, always use the formula Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}.

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Math Problem Analysis

Mathematical Concepts

Distance
Speed
Time Calculation

Formulas

Time = Distance / Speed

Theorems

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Suitable Grade Level

Grades 6-8