Tim charted his distance from home.

Question

Plot the point (12, 18).
x 0-20
y 0-20

a(0,0)
c(2,6)
e(4,4)
g(6,18)
h(18,18)
j(20,0)

How many total minutes did Tim stop to rest?


How many times did Tim get closer to his home?


The speed from the 18th minute to the 20th minute is miles
per minute. (Remember that speed is never negative.)

Answer 1

To analyze Tim's chart based on the description you've provided, let's go through the information given step by step.

1. Plot the Point (12, 18):

   • The coordinates (12, 18) indicate that at time minute 12, Tim was 18 miles away from home. This point will be plotted on the graph, where the X-axis represents time (0-20 minutes) and the Y-axis represents distance from home (0-20 miles).

2. How many total minutes did Tim stop to rest?:

   • To determine the total amount of time Tim stopped, we need to look at the data points you've provided (a, c, e, g, h, j) and see if the y-coordinate (distance) remains constant over any intervals of time. If the distance does not change over a certain number of minutes, it suggests that Tim was resting.
   • Comparing the points:
     • From (0, 0) to (2, 6): distance is increasing
     • From (2, 6) to (4, 4): distance is decreasing
     • From (4, 4) to (6, 18): distance is increasing
     • From (6, 18) to (18, 18): distance stays constant for 12 minutes → Tim was resting.
     • From (18, 18) to (20, 0): distance is decreasing
   • Tim rested for 12 minutes at 18 miles from minute 6 to minute 18.

3. How many times did Tim get closer to his home?:

   • Tim gets closer to home when the y-coordinate decreases as time increases (moving from a higher distance to a lower distance).
   • The intervals where distance decreases (gets closer to home) based on the given points are:
     • From (2, 6) to (4, 4): distance decreases
     • From (18, 18) to (20, 0): distance decreases
   • Therefore, Tim got closer to his home 2 times.

4. Speed from the 18th minute to the 20th minute:

   • At minute 18, Tim is 18 miles away from home (y=18).
   • At minute 20, Tim is 0 miles away from home (y=0).
   • The change in distance is:
     • Distance at 20 min - Distance at 18 min = 0 - 18 = -18 miles
   • The change in time is:
     • 20 min - 18 min = 2 minutes
   • Speed is calculated as total distance traveled divided by total time:
     • Speed = |Change in distance| / Change in time = |−18| / 2 = 18 / 2 = 9 miles per minute.
   • Therefore, the speed from the 18th minute to the 20th minute is 9 miles per minute.

Summary:

• Total minutes Tim stopped to rest: 12 minutes
• Total times Tim got closer to his home: 2 times
• Speed from the 18th minute to the 20th minute: 9 miles per minute