Equations & Inequalities

LESSON 6
Solving Simultaneous Equations Using Substitution
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Paul's mom asks him to stop at the grocery store on his way home from his friend Jacob's house to pick up some ingredients she needs for dinner. The graph below shows the location of all three places Paul will be this afternoon. Find the total distance Paul will travel

1 answer

To calculate the total distance Paul will travel, you'll need the specific coordinates of the three locations: Paul's starting point at Jacob's house, the grocery store, and his home. Here’s a general approach you can follow to find the total distance:

  1. Identify the Coordinates: Let’s denote the locations as follows:

    • Jacob's house: \( (x_1, y_1) \)
    • Grocery store: \( (x_2, y_2) \)
    • Paul's home: \( (x_3, y_3) \)
  2. Calculate Distances:

    • Distance from Jacob's house to the grocery store can be given by the distance formula: \[ d_{JG} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

    • Distance from the grocery store to Paul's home: \[ d_{GH} = \sqrt{(x_3 - x_2)^2 + (y_3 - y_2)^2} \]

  3. Total Distance: The total distance Paul travels will be the sum of both distances: \[ \text{Total Distance} = d_{JG} + d_{GH} \]

Make sure you substitute the actual coordinates from the graph into the equations to find the specific distances. If you provide the coordinates, I can help you calculate the total distance Paul will travel.