Question

Landon left his house at time zero and drove to the store, which is 6 blocks away, at a speed of 3 blocks per minute. Then he stopped and went into the store for 7 minutes. From there, he drove in the same direction at a speed of 2 blocks per minute until he got to the bank, which is 4 blocks away from the store. He stopped at the bank for 5 minutes. Then he drove home at a speed of 5 blocks every minute. Make a graph of showing the number of blocks away from home that Landon is xx minutes after he leaves his house, until he gets back home.

Answer 1

Explanation:

The route Landon took starting at time t = 0 is

Home ⇒ Store ⇒ Bank ⇒ Home

Let's compute cumulative distances(in terms of blocks) and cumulative time using Landon's speed and stay at various places in order to plot a graph. (Note: cumulative means total so far; we add current value to previous total)

The graph will have cumulative time t (in minutes) on the X-axis and cumulative distance d (in terms of blocks) on the Y-axis. We will indicate Landon's position at any time with the coordinates (t, d)

• At time t=0 Landon is at home so d = 0
  Landon's position at time t=0 is (0, 0)

• Home ⇒ Store
  Total distance traveled = 6 blocks at a speed of 3 blocks per minute
  Time taken to reach store = 6/3 = 2 minutes.
  Cumulative time t = 0 + 2 = 2 minutes
  Cumulative distance = 0 + 6 = 6 blocks
  Landon's position is (2, 6)
  
• Landon stayed at the store for 7 minutes. So between t=2 and t=2+7 distance remains unchanged
  Cumulative time = 2 + 7 = 9 minutes
  Cumulative distance = 6 + 0 = 6 blocks
  Landon's position at t = 9 is (9, 6)
  
• Store ⇒ Bank
  Speed was 2 blocks per minute and covered 4 blocks
  So time taken = 2 minutes
  Cumulative time t = 9 + 2 = 11 minutes
  Cumulative distance d = 6 + 4 = 10 blocks.
  So Landon's position is (11 , 10)
  
• Bank Stop : 5 minutes
  Cumulative Time t = 11 + 5 16 minutes
  Cumulative distance d = 10 + 0 = 10 blocks (distance unchanged)
  Landon's position: (16, 10)
  
• Bank ⇒ Home
  Total distance covered = 10 blocks at a speed of 5 blocks per minute
  Time taken = 10/5 = 2 minutes
  Cumulative time t = 16 + 2 = 18 minutes
  Distance from home is 0
  Landon's position is (18, 0)
  
  Plot these boldfaced values on a graph and connect them with line segments to get the graph