1. Jane was vacuuming the narrow hallway in her house. She went 5 feet forward in the first 4 seconds, then went 3 feet backwards in the next 4 seconds. She continued to do this, forward 5 feet in 4 seconds and backwards 3 feet in 4 seconds. If she continues in this way, how many seconds will it take her to reach the end of her hallway, which is 15 feet long?
Pretend that the points in the hallway are marked off in
feet like this:
o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
She starts at 0.
When 4 seconds have lapsed she is at 5.
When 8 seconds have lapsed she is at 2.
When 12 seconds have lapsed she is at 7.
When 16 seconds have lapsed she is at 4.
When 20 seconds have lapsed she is at 9.
When 24 seconds have lapsed she is at 6.
When 28 seconds have lapsed she is at 11.
When 32 seconds have lapsed she is at 8.
When 36 seconds have lapsed she is at 13.
When 40 seconds have lapsed she is at 10.
When 44 seconds have lapsed she is at 15.
So she reaches the end of the hallway in 44 seconds.
Edwin