Question 1177643: 9. At the Fitness place, there are 12 weight machines that Amy liked to use: 6 upper body machines and 6 lower body machines. All machines were in one row, with 8 feet between each upper body machine and 8 feet between each lower body machine. The upper body machines were separated from the lower body machines by 16 feet. The lower body machines were numbered 1 through 6, and the upper body machines were number 7 through 12. Amy started at machine 6 (lower body) and then walked to machine 7 (upper body), then to machine 5 (lower body), then to machine 8 (upper body), and so on, alternating between lower body and upper body. After each 3 lower body machines, she would walk to the mat that was 20 feet past machine 1 and do some stretches. After each 3 upper body machines, she would walk to the wall that was 30 feet past machine 12 and do some stretching. When she finally finished lifting and stretching (the last thing she did was upper body stretching on the wall) how many feet had she walked in all?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down Amy's workout and calculate the total distance she walked.
**1. Amy's Machine Sequence**
Amy's machine sequence is: 6, 7, 5, 8, 4, 9, 3, 10, 2, 11, 1, 12.
**2. Distances Between Machines**
* Lower body machines: 8 feet apart
* Upper body machines: 8 feet apart
* Lower body to upper body transition: 16 feet
**3. Distances to Stretching Areas**
* Lower body mat: 20 feet past machine 1
* Upper body wall: 30 feet past machine 12
**4. Calculate Distances Between Machines**
* 6 to 7: 16 feet
* 7 to 5: 8 + 16 + 8 = 32 feet
* 5 to 8: 16 + 8 + 8 = 32 feet
* 8 to 4: 8 + 16 + 8 = 32 feet
* 4 to 9: 16 + 8 + 8 = 32 feet
* 9 to 3: 8 + 16 + 8 = 32 feet
* 3 to 10: 16 + 8 + 8 = 32 feet
* 10 to 2: 8 + 16 + 8 = 32 feet
* 2 to 11: 16 + 8 + 8 = 32 feet
* 11 to 1: 8 + 16 + 8 = 32 feet
* 1 to 12: 16 + 8 + 8 + 8 + 8 + 8 = 56 feet
**5. Calculate Distances to Stretching Areas**
* After 3 lower body machines (6, 5, 4):
* Distance from machine 4 to machine 1: 3 * 8 = 24 feet
* Distance from machine 1 to mat: 20 feet
* Total distance: 24 + 20 = 44 feet
* After 3 upper body machines (7, 8, 9):
* Distance from machine 9 to machine 12: 3 * 8 = 24 feet
* Distance from machine 12 to wall: 30 feet
* Total distance: 24 + 30 = 54 feet
* After 3 lower body machines (3, 2, 1):
* Distance from machine 1 to mat: 20 feet
* Total distance: 20 feet
* After 3 upper body machines (10, 11, 12):
* Distance from machine 12 to wall: 30 feet
* Total distance: 30 feet
**6. Calculate Total Distance Walked**
* Machine distances: 16 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 56 = 352 feet
* Stretching distances: 44 + 54 + 20 + 30 = 148 feet
* Total distance: 352 + 148 = 500 feet
**Therefore, Amy walked a total of 500 feet.**
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